Run 11332270

Paper: https://arxiv.org/abs/cond-mat/9606089

Formulas:

1-

{(J^{'} / J)}_{c} \approx 0.11

2-

χ (T) = a T^{2}

3-

{Sr}_{0.4} {Ca}_{13.6} {Cu}_{24} O_{41.84}

4-

\hat{ℋ} = J \sum_{⟨ i, j ⟩} 𝐒_{i} \cdot 𝐒_{j} + J^{'} \sum_{⟨ i, j ⟩} 𝐒_{i} \cdot 𝐒_{j},

5-

{(J^{'} / J)}_{c}

6-

0.05 < {(J^{'} / J)}_{c} < 0.12

7-

χ (T) = a T^{2}

8-

0.11 < {(J^{'} / J)}_{c} < 0.12

9-

m = ⟨ a_{i}^{+} a_{i} ⟩

10-

Δ_{1} = ⟨ a_{i} b_{i} ⟩

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1011.4818

Formulas:

1-

e_{↑}^{2} t_{2 ↑}^{3} e_{↓}^{1}

2-

e_{↑}^{2} t_{2 ↑}^{3} e_{↓}^{1}

3-

P b n 21

4-

e^{2} t_{2}^{3}

5-

e^{3} t_{2}^{3}

6-

e_{↑}^{2} t_{2 ↑}^{3} e_{↓}^{1}

7-

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

8-

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

9-

e^{3} t_{2}^{3}

10-

U_{d d} = 5.0

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/physics/0503192

Formulas:

1-

P_{i, R} ≫ P_{i, M} ≫ P_{E}

2-

Q_{i, R} = C_{i} (P_{i, R} - P_{i, M}) ≃ C_{i} P_{i, R}

3-

Q_{i, T} = C_{0} P_{i, M} = Q_{i, R} - P_{i, M} \sum_{j \neq i} C_{j}

4-

Q_{i, T} = Q_{i, R} = C_{i} P_{i, R}

5-

λ_{j, P_{i, R}} < d

6-

λ_{j, P_{i, R}}

7-

σ = 5 \times 10^{11} {(C_{6} / v)}^{2 / 5}

8-

a_{m a x} = \frac{π ℏ Γ}{m λ}

9-

a_{m a x}

10-

a_{m a x}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/nlin/0310016

Formulas:

1-

i \frac{\partial α_{n}}{\partial t} = - (α_{n + 1} + α_{n - 1} - 2 α_{n}) - 2 {∣ α_{n} ∣}^{2} α_{n} + d_{n} α_{n} .

2-

i \frac{\partial α}{\partial t} + \frac{\partial^{2} α}{\partial x^{2}} + 2 {∣ α ∣}^{2} α = d (x) α .

3-

d (x) \equiv 0

4-

α (x, t) = \frac{1}{L} sech \frac{x - v t - x_{0}}{L} e^{i (v x / 2 - ω t)}, ω = \frac{v^{2}}{4} - \frac{1}{L^{2}},

5-

E_{s} = \int_{- \infty}^{\infty} ({∣ \frac{\partial α}{\partial x} ∣}^{2} - {∣ α ∣}^{4}) 𝑑 x = \frac{v^{2}}{2 L} - \frac{2}{3 L^{3}},

6-

E_{d} = \int_{- \infty}^{\infty} d (x) {∣ α ∣}^{2} 𝑑 x

7-

E_{k i n} \sim | E_{d} | ≪ | E_{i n t} |

8-

v^{2} L^{2} \sim 2 | d | L ≪ 1 .

9-

E_{d} = d \int_{- \infty}^{\infty} δ (x) {∣ α ∣}^{2} 𝑑 x = \frac{d}{L^{2}}

10-

E_{k i n} ≫ | E_{d} |

Formulas (html):

Correct Categorie: nlin

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1707.06993

Formulas:

1-

n_{H} \sim 3 \times 10^{- 3}

2-

\sim 1 / σ \approx 10^{17} {cm}^{2}

3-

T_{0} \sim 7 \times 10^{3}

4-

σ = 6.3 \times 10^{18} {cm}^{2}

5-

σ = 1.6 \times 10^{18} {cm}^{2}

6-

M_{\min} = 2 \times 10^{8}

7-

M_{\max} = 5 \times 10^{10}

8-

M_{\min} = 2 \times 10^{8}

9-

x_{HI, th} = 10^{- 2}

10-

≳ 10^{- 12} s^{- 1}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1706.08148

Formulas:

1-

\frac{1}{e + 1} \approx 0.268

2-

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

3-

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

4-

\frac{e}{e + 1} \approx 0.731

5-

\frac{2 k - 1}{3 k - 1}

6-

\frac{e^{1 - \frac{1}{k}}}{e^{1 - \frac{1}{k}} + 1}

7-

\frac{e^{1 - \frac{1}{k}}}{e^{1 - \frac{1}{k}} + 1}

8-

v = (v_{1}, \dots, v_{n})

9-

M (v) = ((x_{1}^{M (v)}, p_{1}^{M (v)}), \dots, (x_{n}^{M (v)}, p_{n}^{M (v)}))

10-

x_{i}^{M (v)}

Formulas (html):

Correct Categorie: cs

Guessed Categorie: quant-ph

Result: incorrect

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: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1810.00213

Formulas:

1-

q_{c} = - Z_{c} e

2-

q_{h} = + Z_{h} e

3-

\frac{\partial N_{c}}{\partial T} + \frac{\partial}{\partial X} (N_{c} U_{c}) = 0,

4-

\frac{\partial U_{c}}{\partial T} + U_{c} \frac{\partial U_{c}}{\partial X} = \frac{Z_{c} e}{m_{c}} \frac{\partial φ}{\partial X},

5-

\frac{\partial N_{h}}{\partial T} + \frac{\partial}{\partial X} (N_{h} U_{h}) = 0,

6-

\frac{\partial U_{h}}{\partial T} + U_{h} \frac{\partial U_{h}}{\partial X} = \frac{Z_{h} e}{m_{h}} \frac{\partial φ}{\partial X} - \frac{1}{m_{h} N_{h}} \frac{\partial P_{h}}{\partial X},

7-

\frac{\partial^{2} φ}{\partial X^{2}} = 4 π e (N_{e} - N_{i} + Z_{c} N_{c} + Z_{h} N_{h}),

8-

n_{c} = N_{c} / n_{c 0}

9-

n_{h} = N_{h} / n_{h 0}

10-

u_{c} = U_{c} / C_{d c}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0902.2706

Formulas:

1-

H = H_{L} + H_{R} + H_{D} + V + W

2-

H_{μ} = \sum_{E} E c_{μ E}^{+} c_{μ E}

3-

H_{D} = \sum_{β} ϵ_{β} d_{β}^{+} d_{β}

4-

\sum_{μ E} \sum_{μ^{'} E^{'}} W_{μ; μ^{'}} e^{i ϕ_{μ μ^{'}}} c_{μ E}^{+} c_{μ^{'} E^{'}}

5-

\sum_{β, β^{'}} \sum_{μ E} \sum_{μ^{'} E^{'}} V_{μ; μ^{'}}^{β; β^{'}} d_{β}^{+} c_{μ E}^{+} c_{μ^{'} E^{'}} d_{β^{'}},

6-

V_{μ; μ^{'}}^{β; β^{'}}

7-

ϕ_{R L} = - ϕ_{L R} = ϕ

8-

ϕ_{L L} = ϕ_{R R} = 0

9-

4 π ℜ [\frac{{(W_{R; L} e^{i ϕ})}^{*} V_{R; R}^{1; 2} V_{R; L}^{2; 1}}{ϵ_{1} + E_{L} - ϵ_{2} - {\tilde{E}}_{R} + i 0^{+}}] δ (E_{L} - E_{R}),

10-

4 π ℜ [\frac{{(V_{R; L}^{2; 1})}^{*} V_{R; R}^{2; 1} W_{R; L} e^{i ϕ}}{E_{L} - E_{R} + i 0^{+}}] δ (E_{L} + ϵ_{1} - {\tilde{E}}_{R} - ϵ_{2}),

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1705.02655

Formulas:

1-

Δ g (x)

2-

Δ g (x)

3-

- 0.8 < η_{1} < 0.8

4-

0.8 < η_{2} < 1.8

5-

Δ g (x)

6-

Δ η \times Δ ϕ = 1 \times 1

7-

E_{T} \geq 0.2 GeV

8-

- 0.8 \leq η \leq 1.8

9-

A_{L L} = \frac{\sum (P_{Y} P_{B}) (N^{+ +} - r N^{+ -})}{\sum {(P_{Y} P_{B})}^{2} (N^{+ +} + r N^{+ -})},

10-

r = ℒ^{+ +} / ℒ^{+ -}

Formulas (html):

Correct Categorie: hep-ex

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/hep-lat/0103024

Formulas:

1-

{γ_{5}, D} = 2 D γ_{5} D

2-

{γ_{5}, D} = 2 D γ_{5} R D

3-

{\frac{d}{d η} \int [d {\bar{ψ}}^{'} d ψ^{'}] e^{- S_{f}^{'}} 𝒪^{'} |}_{η = 0} = 0

4-

ψ^{'} = \exp (i η γ_{5}) ψ

5-

{\bar{ψ}}^{'} = \bar{ψ} \exp (i η γ_{5})

6-

S_{f}^{'} = \bar{ψ^{'}} (D - ζ) ψ^{'}

7-

\frac{1}{2} Tr ({(D - ζ)}^{- 1} {γ_{5}, D}) - ζ Tr ({(D - ζ)}^{- 1} γ_{5}) = 0 .

8-

Tr γ_{5} = 0

9-

{(D - ζ)}^{- 1} = - \sum_{j = 1}^{s} ({(ζ - λ_{j})}^{- 1} P_{j} + \sum_{k = 1}^{d_{j} - 1} {(ζ - λ_{j})}^{- k - 1} Q_{j}^{k}) .

10-

P_{j} P_{l} = δ_{j l} P_{j}

Formulas (html):

Correct Categorie: hep-lat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0112103

Formulas:

1-

λ_{c} = 1.625 μ

2-

Δ λ = 0.36 μ

3-

λ_{c} = 1.630 μ

4-

Δ λ = 0.31 μ

5-

\pm 0 \overset{\circ}{.} 1

6-

Δ K_{S a - b} = 2.61 \pm 0.24

7-

Δ H_{S a - b} = 1.47 \pm 0.05

8-

Δ (H - K) \geq 0.5

9-

0 \overset{''}{.} 082 \pm 0.023

10-

\sim 0 \overset{''}{.} 15

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0912.5266

Formulas:

1-

\frac{1}{2} (N - 1) (N - 2)

2-

\frac{1}{2} N (N - 1)

3-

(\begin{matrix} ν_{e} \\ ν_{μ} \end{matrix}) = (\begin{matrix} \cos θ & e^{i α} \sin θ \\ - e^{- i α} \sin θ & \cos θ \end{matrix}) (\begin{matrix} ν_{1} \\ ν_{2} \end{matrix}) .

4-

| ψ (0) ⟩

5-

A | ν_{e} ⟩ + B | ν_{μ} ⟩

6-

(A \cos θ - B e^{- i α} \sin θ) | ν_{1} ⟩ + (A e^{i α} \sin θ + B \cos θ) | ν_{2} ⟩,

7-

A^{2} + B^{2} = 1

8-

| ψ (t) ⟩ = (A \cos θ - B e^{- i α} \sin θ) | ν_{1} ⟩ + (A e^{i α} \sin θ + B \cos θ) e^{- 2 i δ} | ν_{2} ⟩,

9-

δ = \frac{m_{2}^{2} - m_{1}^{2}}{4 E} t,

10-

P_{ν_{e}} (t) \equiv {| ⟨ ν_{e} | ψ (t) ⟩ |}^{2} .

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0505419

Formulas:

1-

w_{i j} = w_{j i}

2-

s_{i} = \sum_{j \in Γ (i)} w_{i j}

3-

P (k) \sim k^{- γ}

4-

P (w) \sim w^{- θ}

5-

P (s) \sim s^{- α}

6-

Π_{i \to j} = \frac{s_{j} + A}{\sum_{k (\neq i)} (s_{k} + A)} .

7-

P (s) \sim s^{- α}

8-

α = 2 + A / m^{2}

9-

P (w) \sim w^{- θ}

10-

t = N - N_{0}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1804.06360

Formulas:

1-

J_{p g} = q_{e} \int_{E_{g}}^{\infty} Q Y (h ν, E_{g}) ϕ (h ν) d (h ν),

2-

ϕ (h ν)

3-

Q Y (h ν, E_{g})

4-

Q Y (h ν, E_{g})

5-

E Q E (h ν) = C (h ν) (1 - R (h ν)) a (h ν)

6-

C (h ν)

7-

R (h ν)

8-

a (h ν)

9-

R (h ν) = 0

10-

a (h ν) = 1

Formulas (html):

Correct Categorie: physics

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1609.01200

Formulas:

1-

R_{r e d}

2-

R_{r e d}

3-

R_{r e d}

4-

λ_{i m g}

5-

λ_{t o t}

6-

d P = R_{o x} d t

7-

d P = R_{r e d} d t

8-

d t ≪ Δ t

9-

I (V) = \frac{1}{n} \sum_{i = 1}^{n} I (V, i)

10-

Δ t = n * d t

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1908.02727

Formulas:

1-

t \sum_{⟨ i, j ⟩} c_{i}^{†} σ_{0} c_{j} + i λ_{SO} \sum_{⟨ ⟨ i, j ⟩ ⟩} c_{i}^{†} ν_{i, j} σ_{z} c_{j}

2-

+ J \sum_{i} c_{i}^{†} 𝑴_{i} \cdot 𝝈 c_{i} + \sum_{i} c_{i}^{†} V_{i} σ_{0} c_{i} .

3-

ν_{i j} = \frac{2}{\sqrt{3}} (𝒅_{i m} \times 𝒅_{m j}) \cdot 𝒆_{z} = \pm 1

4-

[- \frac{W}{2}, \frac{W}{2}]

5-

λ_{SO} = 0.5 t

6-

L_{x} = (5 N - 1) a

7-

L_{y} = \frac{\sqrt{3}}{2} (N - 1) a

8-

𝑴 = M (\sin θ, 0, \cos θ)

9-

J M / t = 1

10-

E / t = - 0.4

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1912.03647

Formulas:

1-

𝓐 \in ℝ^{n_{1} \times n_{2} \times \dots \times n_{d}}

2-

𝒜 (j_{1}, j_{2}, \dots, j_{d}) = 𝑮_{1} [j_{1}] 𝑮_{2} [j_{2}] \dots 𝑮_{d} [j_{d}]

3-

j_{k} \in {1, 2, \dots, n_{k}}

4-

k \in {1, 2, \dots, d}

5-

𝑮_{k} [j_{k}]

6-

r_{k - 1} \times r_{k}

7-

r_{0} = r_{d} = 1

8-

𝑮_{k} [j_{k}]

9-

𝓖_{k} \in ℝ^{n_{k} \times r_{k - 1} \times r_{k}}

10-

𝓐 = 𝓖_{1} \times^{1} 𝓖_{2} \times^{1} \dots \times^{1} 𝓖_{d}

Formulas (html):

Correct Categorie: cs

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/quant-ph/0210044

Formulas:

1-

ϵ (Q) η (P) \geq \frac{ℏ}{2} .

2-

Q P - P Q = i ℏ

3-

σ (A) σ (B) \geq \frac{1}{2} | ⟨ ψ, [A, B] ψ ⟩ |

4-

σ (A), σ (B) < \infty

5-

[A, B] = A B - B A

6-

σ (A) = {(⟨ ψ, A^{2} ψ ⟩ - {⟨ ψ, A ψ ⟩}^{2})}^{1 / 2}

7-

[Q, P] = i ℏ

8-

σ (Q) σ (P) \geq \frac{ℏ}{2},

9-

(0, Δ t)

10-

D (P) = P (Δ t) - P (0),

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/0910.0193

Formulas:

1-

p p \to H \to W W \to e ν μ ν

2-

135 < m_{H} < 190

3-

160 < m_{H} < 170

4-

g g \to H \to W W

5-

q q / q g \to W W

6-

g g \to W W

7-

p p \to t \bar{t}

8-

H \to W W \to ℓ ν ℓ ν

9-

E_{T}^{m i s s} > 30

10-

| M_{τ τ} - M_{Z} | < 25

Formulas (html):

Correct Categorie: hep-ex

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1701.00582

Formulas:

1-

\sqrt{3} N \times \sqrt{3} N

2-

3 N \times 3 N

3-

\sqrt{3} N \times \sqrt{3} N

4-

3 N \times 3 N

5-

\sqrt{3} N \times \sqrt{3} N

6-

3 N \times 3 N

7-

H = - \sum_{⟨ i, j ⟩} t_{i, j} c_{i}^{†} c_{j} + \sum_{i} u_{i} c_{i}^{†} c_{i},

8-

T (E) = Tr [Γ_{L} G^{r} Γ_{R} G^{a}],

9-

G^{r} = {[E - H - Σ^{r}]}^{- 1}

10-

G^{a} = {(G^{r})}^{†}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1806.03780

Formulas:

1-

{⟨ N^{2} ⟩}^{1 / 2}

2-

μ (θ, ω) = \Pr {Θ = θ, Ω = ω}

3-

ϵ_{G} {(μ)}^{2} = \sum_{ω, θ} {(ω - θ)}^{2} μ (θ, ω),

4-

ϵ_{G} (μ) = {⟨ N^{2} ⟩}^{1 / 2}

5-

ϵ_{G} (μ) = 0

6-

\sum {μ (θ, ω) ∣ θ = ω} = 1

7-

U {(τ)}^{†} (I \otimes M) U (τ),

8-

\exp (- i τ H / ℏ) .

9-

N (A, 𝐌) = M (τ) - A (0)

10-

ϵ_{N O} (A, 𝐌, | ψ ⟩) = {⟨ ψ, ξ | N {(A, 𝐌)}^{2} | ψ, ξ ⟩}^{1 / 2},

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/0709.1177

Formulas:

1-

(10^{21} eV)

2-

\sim ZeV (= 10^{21} eV)

3-

| B | > | E |

4-

ω^{2} = k^{2} c^{2} + \frac{ω_{i p}^{2}}{1 \pm ω_{i c} / ω} + \frac{ω_{p}^{2}}{1 \mp ω_{c} / ω},

5-

ω_{p} = \sqrt{4 π e^{2} n_{p} / m_{e}}

6-

ω_{c} = e B / m_{e} c

7-

F_{z} = - \frac{1}{2} \frac{e^{2}}{m_{e} ω (ω - ω_{c})} [1 + \frac{k v_{g} ω_{c}}{ω (ω - ω_{c})}] \partial_{ζ} E_{_{W}}^{2} (ζ),

8-

E_{_{W}} (ζ)

9-

ζ \equiv z - v_{g} t

10-

E_{z} (ζ) = - \frac{e k_{p} E_{_{W}}^{2}}{m_{e} ω (ω - ω_{c})} [1 + \frac{k v_{g} ω_{c}}{ω (ω - ω_{c})}] χ (ζ),

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1701.09047

Formulas:

1-

C_{ℓ}^{A \times B} = C_{ℓ}^{A \times B - P} + C_{ℓ}^{A \times B - C},

2-

C_{ℓ}^{A \times B - P}

3-

C_{ℓ}^{A \times B - C}

4-

\frac{d^{2} N}{d M d V}

5-

C_{ℓ}^{A \times B - P} = 4 π \int d z \frac{d V}{d z d Ω} \int d M \frac{d^{2} N}{d M d V} W_{A}^{P} W_{B}^{P} .

6-

W_{tSZ}^{P} = Y_{500} y_{ℓ},

7-

E^{- β_{sz}} (z) [\frac{D_{a n g}^{2} (z) Y_{500}}{10^{- 4} {Mpc}^{2}}] = Y_{⋆} {[\frac{h}{0.7}]}^{- 2 + α_{sz}} {[\frac{(1 - b) M_{500}}{6 \times 10^{14} M_{⊙}}]}^{α_{sz}},

8-

E (z) = Ω_{m} {(1 + z)}^{3} + Ω_{Λ}

9-

W_{ϕ}^{P} = - 2 ψ_{ℓ} \frac{(χ^{'} - χ) χ}{χ^{'}},

10-

Δ ψ = \frac{3}{2} Ω_{m} H_{0}^{2} \frac{δ}{a},

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0902.3682

Formulas:

1-

p_{R} = 0.05 \pm 0.02

2-

r_{e} = 1.9 \pm 0.3

3-

p_{R} = 0.06 \pm 0.02

4-

r_{e} = 2.0 \pm 0.2

5-

14 \overset{''}{.} 7

6-

H_{R} = 15.49 \pm 0.05

7-

m_{R} (1, 1, 0) = 15.69 \pm 0.05

8-

H_{R} = 15.10 \pm 0.05

9-

m_{R} (1, 1, 0) = 15.27 \pm 0.05

10-

P_{r o t} = 3.471

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0604410

Formulas:

1-

I (D, T) = I (D | T) + I (T)

2-

I (D, T)

3-

I_{A} (D, T) = - \ln ℒ + k .

4-

I_{B} (T) = \frac{k}{2} \ln N

5-

Δ I (D | T) \approx Δ χ^{2} / 2 = - 4

6-

Δ I (D, T) = - 3

7-

Δ I (D, T) \approx 0

8-

I (T) = 0

9-

I (D, T) = I (D | T)

10-

σ_{S}^{2} = \frac{1}{N} \sum x_{i}^{2}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1503.04461

Formulas:

1-

θ_{t t} (t, x) - K (0) Δ θ (t, x) - \int_{0}^{t} K^{'} (t - s) Δ θ (s, x) 𝑑 s = u (t, x), x \in Ω, t > 0 .

2-

{θ |}_{t = 0} = φ_{0} (x), {θ_{t} |}_{t = 0} = φ_{1} (x),

3-

{θ |}_{\partial Ω} = 0,

4-

K (t) = \sum_{j = 1}^{N} \frac{c_{j}}{γ_{j}} e^{- γ_{j} t},

5-

u (t, x)

6-

| u (t, x) | \leq M

7-

θ (t, x)

8-

θ_{t} (t, x)

9-

u (t, x) \in C ([0, \infty), L_{2} (0, π))

10-

\frac{\partial}{\partial t} (θ_{t} (t, x) - \int_{0}^{t} K (t - s) θ_{x x} (s, x) 𝑑 s - \int_{0}^{t} u (s, x) 𝑑 s) = 0 .

Formulas (html):

Correct Categorie: math

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0901.1982

Formulas:

1-

\sim (1 - 3) \times 10^{5} r_{g}

2-

(4 - 7) r_{g}

3-

10^{4 - 5} r_{g}

4-

r_{g} \equiv G M / c^{2}

5-

H R 2 < 1.1

6-

H R 2 = 1.1

7-

f = 1 - \exp (- 7.5 R)

8-

1 / (1 - f) ≃ 1 + 7.5 R

9-

N_{H} = 3 \times 10^{21}

10-

Q = ν_{0} / FWHM \approx 11

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0505166

Formulas:

1-

{< σ_{00} σ_{m n} >}^{[4], [5], [6]}

2-

S_{n} = < σ_{00} σ_{n n} >

3-

n = 6^{[8]}

4-

H = - \sum_{i, j \in Z^{2}} (J_{1} σ_{i, j} σ_{i + 1, j} + J_{2} σ_{i, j} σ_{i, j + 1})

5-

β = {(k_{B} T)}^{- 1}

6-

k_{>} = s i n h (2 β J_{1}) s i n h (2 β J_{2})

7-

k_{<} = k_{>}^{- 1}

8-

k_{>} (β_{c}) = k_{<} (β_{c}) = 1

9-

t = {\begin{matrix} k_{>}^{- 2} f o r T > T_{c} \\ k_{<}^{- 2} f o r T < T_{c} \end{matrix}

10-

< σ_{00} σ_{n n} >

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0912.2117

Formulas:

1-

{YBa}_{2} {Cu}_{3} O_{7 - δ}

2-

V_{n} = V_{n}^{'} - i V_{n}^{''}

3-

{YBa}_{2} {Cu}_{3} O_{7 - δ}

4-

J_{c} (T)

5-

J_{c} (T)

6-

J_{c} \propto {(1 - T / T_{c})}^{n}

7-

J_{c} (T)

8-

{YBa}_{2} {Cu}_{3} O_{7 - δ}

9-

V_{n} = V_{n}^{'} - i V_{n}^{''}

10-

n = 1, 3, 5 \dots

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1110.6473

Formulas:

1-

⌊ (3 n - 9) / 5 ⌋

2-

O (n^{2})

3-

O (n^{2})

4-

O (\log n)

5-

⌊ (3 n - 9) / 5 ⌋

6-

(3 n - 10) / 5 = ⌊ (3 n - 9) / 5 ⌋

7-

⌊ (3 n - 9) / 5 ⌋

8-

⌊ (3 n - 9) / 5 ⌋

9-

⌊ (3 n - 6) / 5 ⌋

10-

⌊ (3 n - 9) / 5 ⌋

Formulas (html):

Correct Categorie: cs

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0104119

Formulas:

1-

λ = \frac{\sqrt{κ / Y}}{X} = \frac{1}{\sqrt{12 (1 - ν^{2})}} (\frac{h}{X}),

2-

\nabla^{4} f = [χ, f] + P, λ^{2} \nabla^{4} χ = - \frac{1}{2} [f, f],

3-

[a, b] = ϵ_{α μ} ϵ_{β ν} (\partial_{α} \partial_{β} a) (\partial_{μ} \partial_{ν} b),

4-

C_{α β} = X^{- 1} \partial_{α} \partial_{β} f

5-

σ_{α β} = κ X^{- 2} ϵ_{α μ} ϵ_{β ν} \partial_{μ} \partial_{ν} χ .

6-

\partial_{α} σ_{α β} = 0

7-

f = α | y / X |

8-

f = λ^{1 / 3} \tilde{f}, χ = λ^{- 2 / 3} \tilde{χ}, y = λ^{1 / 3} X \tilde{y}, x = X \tilde{x},

9-

σ_{x x}^{(o)} = F_{o} δ (y) .

10-

σ_{x x}^{(o)}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1311.3644

Formulas:

1-

| A^{- 1} \cap B | \leq 2 | B | / q - 2

2-

| B | \leq q^{3}

3-

| A^{- 1} \cap B | \leq | B | / q \cdot (1 + O_{d} (q^{- 1 / 2}))

4-

| B | = q^{d}

5-

| B | \leq q^{3}

6-

| A^{- 1} \cap B |

7-

| A^{- 1} \cap B | \leq 2 | B | / q - 2

8-

| A^{- 1} \cap B | \leq 3 | B | / 4 - 1

9-

2 | B | / q - 2

10-

| B | \leq q^{2}

Formulas (html):

Correct Categorie: math

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/nucl-th/0501058

Formulas:

1-

H = - \frac{ℏ^{2}}{2 m_{α}} (\nabla_{1}^{2} + \nabla_{2}^{2} + \nabla_{3}^{2}) + V (r_{23}) + V (r_{31}) + V (r_{12}),

2-

𝒓_{i j} = 𝒓_{j} - 𝒓_{i}

3-

V (r_{i j})

4-

\tilde{V} (𝒓_{i j}) = V (r_{i j}) + Λ \sum_{f} {\hat{Γ}}_{i j}^{(f)},

5-

{\hat{Γ}}_{i j}^{(f)} = \sum_{m_{f}} | φ_{f m_{f}} ⟩ ⟨ φ_{f m_{f}} |,

6-

φ_{f m_{f}} (𝒓_{i j})

7-

ℏ^{2} / m_{α} = 10.4465

8-

V_{C} (r) = 4 e^{2} \erf (β r) / r .

9-

V_{AB} (r) = V_{1} \exp (- η_{1} r^{2}) + V_{2} \exp (- η_{2} r^{2}) + V_{C} (r) .

10-

β = \sqrt{3} / (2 \times 1.44)

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0304563

Formulas:

1-

F_{ν} \propto ν^{- β} t^{- α}

2-

α_{1} = 0.93 \pm 0.04

3-

α_{2} = 1.90 \pm 0.03

4-

1.6 \times 10^{- 4} erg {cm}^{- 2}

5-

E_{γ, iso} \sim 1 \times 10^{52}

6-

F_{X} = 1.4 \times 10^{- 10} erg \sec^{- 1} {cm}^{- 2}

7-

L_{X, iso} \sim 5 \times 10^{45} erg \sec^{- 1}

8-

θ_{j, 0} = 0.07

9-

f_{b} \approx θ_{j, o}^{2} / 2 \approx 1 / 400

10-

E_{γ} \sim 3 \times 10^{49}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1404.1013

Formulas:

1-

t \to W b \to l ν + (J / ψ + X)

2-

J / ψ \to μ^{+} μ^{-}

3-

m_{t}^{p o l e} \pm 1.00

4-

α (m_{Z})

5-

t \to W b \to j j b

6-

R = m_{j j b} / m_{j j}

7-

m_{j j b}

8-

ℒ_{i n t e g r a t e d}

9-

e t a l .

10-

t \to W b \to ℓ ν J / ψ X

Formulas (html):

Correct Categorie: hep-ex

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1309.5221

Formulas:

1-

\partial_{t} (ρ_{\pm} γ_{\pm}) + \nabla_{i} (ρ_{\pm} u_{\pm}^{i}) = 0,

2-

\partial_{t} (w_{\pm} γ_{\pm}^{2} - p_{\pm}) + \nabla_{i} (w_{\pm} γ_{\pm} u_{\pm}^{i}) = (j_{\pm}^{i} E_{i}) \pm ϰ_{f} c^{2} n_{+} n_{-} (γ_{-} - γ_{+}),

3-

\partial_{t} ((w_{\pm} / c^{2}) γ_{\pm} u_{\pm}^{s}) + \nabla_{i} ((w_{\pm} / c^{2}) u_{\pm}^{i} u_{\pm}^{s} + g^{i s} p_{\pm}) = q_{\pm} E^{s} + \frac{1}{c} e^{s i k} j_{i}^{\pm} B_{k} \pm ϰ_{f} n_{+} n_{-} (u_{-}^{s} - u_{+}^{s}),

4-

\nabla_{i} B^{i} = 0,

5-

\frac{1}{c} \partial_{t} B^{s} + e^{s i k} \partial_{i} E_{k} = 0,

6-

\nabla_{i} E^{i} = 4 π (q_{+} + q_{-}),

7-

\frac{1}{c} \partial_{t} E^{s} - e^{s i k} \partial_{i} B_{k} = - \frac{4 π}{c} (j_{+}^{s} + j_{-}^{s}) .

8-

ρ_{\pm} = m_{e} n_{\pm}

9-

𝒖_{\pm} = γ_{\pm} 𝒗_{\pm}

10-

q_{\pm} = \pm e γ_{\pm} n_{\pm}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/gr-qc/0505029

Formulas:

1-

h_{rss} \sim 10^{- 20} - 10^{- 19}

2-

h_{rss} \sim 10^{- 20} - 10^{- 19}

3-

s (t) = [Δ L_{x} (t) - Δ L_{y} (t)] / L

4-

y_{i j} = - \ln (\frac{R_{i j}}{n P}) .

5-

{\tilde{y}}_{i j} = g_{P} ({\tilde{w}}_{i j}) \equiv \ln (P) - \ln (\sqrt{2 / π} \int_{{\tilde{w}}_{i j}}^{\infty} e^{- x^{2} / 2} 𝑑 x),

6-

w_{i j} = g_{P}^{- 1} (y_{i j}),

7-

ρ_{i j} = w_{i j}^{2} - 1,

8-

y_{(i - 1) j}^{'} + y_{i j}^{'} + y_{(i + 1) j}^{'} > η,

9-

ρ = \sum_{i j \in C} ρ_{i j}, Y = \sum_{i j \in C} y_{i j} .

10-

T = \sum_{i j \in C} t_{i} w_{i j}^{2} / \sum_{i j \in C} w_{i j}^{2} .

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: quant-ph

Result: incorrect

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

Formulas:

1-

ρ = 1.06 g / c m^{3}

2-

g (τ) = \frac{1}{\sqrt{π w^{2}}} \exp (- \frac{τ^{2}}{w^{2}}) .

3-

k (τ) = \frac{2}{\sqrt{π} w^{3}} (\frac{2 τ^{2}}{w^{2}} - 1) \exp (- \frac{τ^{2}}{w^{2}}) .

4-

A (\frac{2 τ^{2}}{w^{2}} - 1) \exp (- \frac{τ^{2}}{w^{2}}) + B if | τ | ⩽ L

5-

k ⋆ τ^{2} = 2

6-

L ≫ w ≫ 1 / F_{s}

7-

P (a) = C \exp (- a^{2} / (1 + {| \frac{a β}{σ} |}^{γ}) σ^{2})

8-

| a | < 10 {⟨ a^{2} ⟩}^{1 / 2}

9-

| a | < 40 {⟨ a^{2} ⟩}^{1 / 2}

10-

a^{4} P (a)

Formulas (html):

Correct Categorie: physics

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/9609172

Formulas:

1-

x (T) - x_{s}

2-

x (T) < x_{s}

3-

𝒞 (x_{0}, x_{s}, T) = \int_{x_{s}}^{\infty} 𝑑 x^{'} (x^{'} - x_{s}) P (x^{'}, T | x_{0}, 0)

4-

P (x^{'}, T | x_{0}, 0)

5-

P (x^{'}, T | x_{0}, 0)

6-

x (T) = x_{0} + \sum_{k = 0}^{\frac{T}{τ} - 1} δ x_{k}

7-

δ x_{k} = ϵ_{k} γ_{k}

8-

{(ϵ_{k})}_{k \geq 0}

9-

{(γ_{k})}_{k \geq 0}

10-

P (δ x_{k}) \equiv \frac{1}{γ_{k}} P_{0} (\frac{δ x_{k}}{γ_{k}})

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1302.2896

Formulas:

1-

δ r^{2} (t) \sim t^{x}

2-

U_{F, M} (r) = μ_{0} χ_{F, M}^{2} B^{2} / (4 π r^{3})

3-

(Φ_{M}, Φ_{F})

4-

σ_{F, M} = σ_{F, M}^{0} + \int_{σ_{F, M}^{0}}^{\infty} (1 - e^{- β U_{F, M} (r)}) d r

5-

β = 1 / k_{B} T

6-

(Φ_{F}, Φ_{M})

7-

S (k) = \frac{1}{N_{M}} ⟨ \sum_{i = 1}^{N_{M}} \sum_{j = 1}^{N_{M}} e^{- i \vec{k} \cdot ({\vec{r}}_{i} - {\vec{r}}_{j})} ⟩

8-

δ r^{2} (t) = \frac{1}{N_{F}} ⟨ \sum_{i = 1}^{N_{F}} {[{\vec{r}}_{i} (t) - {\vec{r}}_{i} (0)]}^{2} ⟩

9-

σ_{M} \in [0.85, 1.15]

10-

ρ = 0.278 σ_{M}^{- 2}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1009.1224

Formulas:

1-

E_{jet} = E_{iso} θ^{2} / 2 ergs

2-

E_{iso} = 2.6 \times 10^{51} ergs

3-

n = 0.78 {cm}^{- 3}

4-

γ_{s h} = 25

5-

γ ≃ 25 / \sqrt{2} ≃ 17.7

6-

R_{0} ≃ 2.68 \times 10^{- 2} pc

7-

t_{local, 0} ≃ 51.68 days

8-

t_{obs, 0} = R_{0} / 2 γ^{2} c ≃ 1 hour

9-

Δ R ≃ R_{0} / γ^{2} = 8.5 \times 10^{- 5} pc

10-

[1.57 \times 10^{- 2}, 1.57] pc

Formulas (html):

<math><mrow id="S2.p1.2.m2.1.1" xref="S2.p1.2.m2.1.1.cmml"><mpadded width="+1.7pt" id="S2.p1.2.m2.1.1.2" xref="S2.p1.2.m2.1.1.2.cmml"><msub id="S2.p1.2.m2.1.1.2a" xref="S2.p1.2.m2.1.1.2.cmml"><mi id="S2.p1.2.m2.1.1.2.2" xref="S2.p1.2.m2.1.1.2.2.cmml">E</mi><mi id="S2.p1.2.m2.1.1.2.3" xref="S2.p1.2.m2.1.1.2.3.cmml">jet</mi></msub></mpadded><mo rspace="4.2pt" id="S2.p1.2.m2.1.1.1" xref="S2.p1.2.m2.1.1.1.cmml">=</mo><mrow id="S2.p1.2.m2.1.1.3" xref="S2.p1.2.m2.1.1.3.cmml"><mrow id="S2.p1.2.m2.1.1.3.2" xref="S2.p1.2.m2.1.1.3.2.cmml"><mrow id="S2.p1.2.m2.1.1.3.2.2" xref="S2.p1.2.m2.1.1.3.2.2.cmml"><msub id="S2.p1.2.m2.1.1.3.2.2.2" xref="S2.p1.2.m2.1.1.3.2.2.2.cmml"><mi id="S2.p1.2.m2.1.1.3.2.2.2.2" xref="S2.p1.2.m2.1.1.3.2.2.2.2.cmml">E</mi><mi id="S2.p1.2.m2.1.1.3.2.2.2.3" xref="S2.p1.2.m2.1.1.3.2.2.2.3.cmml">iso</mi></msub><mo id="S2.p1.2.m2.1.1.3.2.2.1" xref="S2.p1.2.m2.1.1.3.2.2.1.cmml">⁢</mo><msup id="S2.p1.2.m2.1.1.3.2.2.3" xref="S2.p1.2.m2.1.1.3.2.2.3.cmml"><mi id="S2.p1.2.m2.1.1.3.2.2.3.2" xref="S2.p1.2.m2.1.1.3.2.2.3.2.cmml">θ</mi><mn id="S2.p1.2.m2.1.1.3.2.2.3.3" xref="S2.p1.2.m2.1.1.3.2.2.3.3.cmml">2</mn></msup></mrow><mo id="S2.p1.2.m2.1.1.3.2.1" xref="S2.p1.2.m2.1.1.3.2.1.cmml">/</mo><mpadded width="+1.7pt" id="S2.p1.2.m2.1.1.3.2.3" xref="S2.p1.2.m2.1.1.3.2.3.cmml"><mn id="S2.p1.2.m2.1.1.3.2.3a" xref="S2.p1.2.m2.1.1.3.2.3.cmml">2</mn></mpadded></mrow><mo id="S2.p1.2.m2.1.1.3.1" xref="S2.p1.2.m2.1.1.3.1.cmml">⁢</mo><mi id="S2.p1.2.m2.1.1.3.3" xref="S2.p1.2.m2.1.1.3.3.cmml">ergs</mi></mrow></mrow></math>, <math><mrow id="S2.p1.3.m3.1.1" xref="S2.p1.3.m3.1.1.cmml"><mpadded width="+1.7pt" id="S2.p1.3.m3.1.1.2" xref="S2.p1.3.m3.1.1.2.cmml"><msub id="S2.p1.3.m3.1.1.2a" 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">E</mi><mi id="S2.p1.3.m3.1.1.2.3" xref="S2.p1.3.m3.1.1.2.3.cmml">iso</mi></msub></mpadded><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"><mrow id="S2.p1.3.m3.1.1.3.2" xref="S2.p1.3.m3.1.1.3.2.cmml"><mn id="S2.p1.3.m3.1.1.3.2.2" xref="S2.p1.3.m3.1.1.3.2.2.cmml"> 2.6</mn><mo id="S2.p1.3.m3.1.1.3.2.1" xref="S2.p1.3.m3.1.1.3.2.1.cmml">×</mo><mpadded width="+1.7pt" id="S2.p1.3.m3.1.1.3.2.3" xref="S2.p1.3.m3.1.1.3.2.3.cmml"><msup id="S2.p1.3.m3.1.1.3.2.3a" xref="S2.p1.3.m3.1.1.3.2.3.cmml"><mn id="S2.p1.3.m3.1.1.3.2.3.2" xref="S2.p1.3.m3.1.1.3.2.3.2.cmml">10</mn><mn id="S2.p1.3.m3.1.1.3.2.3.3" xref="S2.p1.3.m3.1.1.3.2.3.3.cmml">51</mn></msup></mpadded></mrow><mo id="S2.p1.3.m3.1.1.3.1" xref="S2.p1.3.m3.1.1.3.1.cmml">⁢</mo><mi id="S2.p1.3.m3.1.1.3.3" xref="S2.p1.3.m3.1.1.3.3.cmml">ergs</mi></mrow></mrow></math>, <math><mrow id="S2.p1.4.m4.1.1" xref="S2.p1.4.m4.1.1.cmml"><mpadded width="+1.7pt" id="S2.p1.4.m4.1.1.2" xref="S2.p1.4.m4.1.1.2.cmml"><mi id="S2.p1.4.m4.1.1.2a" xref="S2.p1.4.m4.1.1.2.cmml">n</mi></mpadded><mo id="S2.p1.4.m4.1.1.1" xref="S2.p1.4.m4.1.1.1.cmml">=</mo><mrow id="S2.p1.4.m4.1.1.3" xref="S2.p1.4.m4.1.1.3.cmml"><mn id="S2.p1.4.m4.1.1.3.2" xref="S2.p1.4.m4.1.1.3.2.cmml"> 0.78</mn><mo id="S2.p1.4.m4.1.1.3.1" xref="S2.p1.4.m4.1.1.3.1.cmml">⁢</mo><msup id="S2.p1.4.m4.1.1.3.3" xref="S2.p1.4.m4.1.1.3.3.cmml"><mi id="S2.p1.4.m4.1.1.3.3.2" xref="S2.p1.4.m4.1.1.3.3.2.cmml">cm</mi><mrow id="S2.p1.4.m4.1.1.3.3.3" xref="S2.p1.4.m4.1.1.3.3.3.cmml"><mo id="S2.p1.4.m4.1.1.3.3.3.1" xref="S2.p1.4.m4.1.1.3.3.3.1.cmml">-</mo><mn id="S2.p1.4.m4.1.1.3.3.3.2" xref="S2.p1.4.m4.1.1.3.3.3.2.cmml">3</mn></mrow></msup></mrow></mrow></math>, <math><mrow id="S2.p1.5.m5.1.1" xref="S2.p1.5.m5.1.1.cmml"><mpadded width="+1.7pt" id="S2.p1.5.m5.1.1.2" xref="S2.p1.5.m5.1.1.2.cmml"><msub id="S2.p1.5.m5.1.1.2a" xref="S2.p1.5.m5.1.1.2.cmml"><mi id="S2.p1.5.m5.1.1.2.2" xref="S2.p1.5.m5.1.1.2.2.cmml">γ</mi><mrow id="S2.p1.5.m5.1.1.2.3" xref="S2.p1.5.m5.1.1.2.3.cmml"><mi id="S2.p1.5.m5.1.1.2.3.2" xref="S2.p1.5.m5.1.1.2.3.2.cmml">s</mi><mo id="S2.p1.5.m5.1.1.2.3.1" xref="S2.p1.5.m5.1.1.2.3.1.cmml">⁢</mo><mi id="S2.p1.5.m5.1.1.2.3.3" xref="S2.p1.5.m5.1.1.2.3.3.cmml">h</mi></mrow></msub></mpadded><mo id="S2.p1.5.m5.1.1.1" xref="S2.p1.5.m5.1.1.1.cmml">=</mo><mn id="S2.p1.5.m5.1.1.3" xref="S2.p1.5.m5.1.1.3.cmml"> 25</mn></mrow></math>, <math><mrow id="S2.p1.6.m6.1.1" xref="S2.p1.6.m6.1.1.cmml"><mi id="S2.p1.6.m6.1.1.2" xref="S2.p1.6.m6.1.1.2.cmml">γ</mi><mo id="S2.p1.6.m6.1.1.3" xref="S2.p1.6.m6.1.1.3.cmml">≃</mo><mrow id="S2.p1.6.m6.1.1.4" xref="S2.p1.6.m6.1.1.4.cmml"><mn id="S2.p1.6.m6.1.1.4.2" xref="S2.p1.6.m6.1.1.4.2.cmml">25</mn><mo id="S2.p1.6.m6.1.1.4.1" xref="S2.p1.6.m6.1.1.4.1.cmml">/</mo><msqrt id="S2.p1.6.m6.1.1.4.3" xref="S2.p1.6.m6.1.1.4.3.cmml"><mn id="S2.p1.6.m6.1.1.4.3.2" xref="S2.p1.6.m6.1.1.4.3.2.cmml">2</mn></msqrt></mrow><mo id="S2.p1.6.m6.1.1.5" xref="S2.p1.6.m6.1.1.5.cmml">≃</mo><mn id="S2.p1.6.m6.1.1.6" xref="S2.p1.6.m6.1.1.6.cmml">17.7</mn></mrow></math>, <math><mrow id="S2.p1.7.m7.1.1" xref="S2.p1.7.m7.1.1.cmml"><mpadded width="+1.7pt" id="S2.p1.7.m7.1.1.2" xref="S2.p1.7.m7.1.1.2.cmml"><msub id="S2.p1.7.m7.1.1.2a" xref="S2.p1.7.m7.1.1.2.cmml"><mi id="S2.p1.7.m7.1.1.2.2" xref="S2.p1.7.m7.1.1.2.2.cmml">R</mi><mn id="S2.p1.7.m7.1.1.2.3" xref="S2.p1.7.m7.1.1.2.3.cmml">0</mn></msub></mpadded><mo id="S2.p1.7.m7.1.1.1" xref="S2.p1.7.m7.1.1.1.cmml">≃</mo><mrow id="S2.p1.7.m7.1.1.3" xref="S2.p1.7.m7.1.1.3.cmml"><mrow id="S2.p1.7.m7.1.1.3.2" xref="S2.p1.7.m7.1.1.3.2.cmml"><mpadded width="+1.7pt" id="S2.p1.7.m7.1.1.3.2.2" xref="S2.p1.7.m7.1.1.3.2.2.cmml"><mn id="S2.p1.7.m7.1.1.3.2.2a" xref="S2.p1.7.m7.1.1.3.2.2.cmml"> 2.68</mn></mpadded><mo id="S2.p1.7.m7.1.1.3.2.1" xref="S2.p1.7.m7.1.1.3.2.1.cmml">×</mo><mpadded width="+1.7pt" id="S2.p1.7.m7.1.1.3.2.3" xref="S2.p1.7.m7.1.1.3.2.3.cmml"><msup id="S2.p1.7.m7.1.1.3.2.3a" xref="S2.p1.7.m7.1.1.3.2.3.cmml"><mn id="S2.p1.7.m7.1.1.3.2.3.2" xref="S2.p1.7.m7.1.1.3.2.3.2.cmml"> 10</mn><mrow id="S2.p1.7.m7.1.1.3.2.3.3" xref="S2.p1.7.m7.1.1.3.2.3.3.cmml"><mo id="S2.p1.7.m7.1.1.3.2.3.3.1" xref="S2.p1.7.m7.1.1.3.2.3.3.1.cmml">-</mo><mn id="S2.p1.7.m7.1.1.3.2.3.3.2" xref="S2.p1.7.m7.1.1.3.2.3.3.2.cmml">2</mn></mrow></msup></mpadded></mrow><mo id="S2.p1.7.m7.1.1.3.1" xref="S2.p1.7.m7.1.1.3.1.cmml">⁢</mo><mi id="S2.p1.7.m7.1.1.3.3" xref="S2.p1.7.m7.1.1.3.3.cmml">pc</mi></mrow></mrow></math>, <math><mrow id="S2.p1.8.m8.2.3" xref="S2.p1.8.m8.2.3.cmml"><mpadded width="+1.7pt" id="S2.p1.8.m8.2.3.2" xref="S2.p1.8.m8.2.3.2.cmml"><msub id="S2.p1.8.m8.2.3.2a" xref="S2.p1.8.m8.2.3.2.cmml"><mi id="S2.p1.8.m8.2.3.2.2" xref="S2.p1.8.m8.2.3.2.2.cmml">t</mi><mrow id="S2.p1.8.m8.2.2.2.4" xref="S2.p1.8.m8.2.2.2.3.cmml"><mi id="S2.p1.8.m8.1.1.1.1" xref="S2.p1.8.m8.1.1.1.1.cmml">local</mi><mo id="S2.p1.8.m8.2.2.2.4.1" xref="S2.p1.8.m8.2.2.2.3.cmml">,</mo><mn id="S2.p1.8.m8.2.2.2.2" xref="S2.p1.8.m8.2.2.2.2.cmml">0</mn></mrow></msub></mpadded><mo id="S2.p1.8.m8.2.3.1" xref="S2.p1.8.m8.2.3.1.cmml">≃</mo><mrow id="S2.p1.8.m8.2.3.3" xref="S2.p1.8.m8.2.3.3.cmml"><mpadded width="+1.7pt" id="S2.p1.8.m8.2.3.3.2" xref="S2.p1.8.m8.2.3.3.2.cmml"><mn id="S2.p1.8.m8.2.3.3.2a" xref="S2.p1.8.m8.2.3.3.2.cmml"> 51.68</mn></mpadded><mo id="S2.p1.8.m8.2.3.3.1" xref="S2.p1.8.m8.2.3.3.1.cmml">⁢</mo><mi id="S2.p1.8.m8.2.3.3.3" xref="S2.p1.8.m8.2.3.3.3.cmml">days</mi></mrow></mrow></math>, <math><mrow id="S2.p1.9.m9.2.3" xref="S2.p1.9.m9.2.3.cmml"><mpadded width="+1.7pt" id="S2.p1.9.m9.2.3.2" xref="S2.p1.9.m9.2.3.2.cmml"><msub id="S2.p1.9.m9.2.3.2a" xref="S2.p1.9.m9.2.3.2.cmml"><mi id="S2.p1.9.m9.2.3.2.2" xref="S2.p1.9.m9.2.3.2.2.cmml">t</mi><mrow id="S2.p1.9.m9.2.2.2.4" xref="S2.p1.9.m9.2.2.2.3.cmml"><mi id="S2.p1.9.m9.1.1.1.1" xref="S2.p1.9.m9.1.1.1.1.cmml">obs</mi><mo id="S2.p1.9.m9.2.2.2.4.1" xref="S2.p1.9.m9.2.2.2.3.cmml">,</mo><mn id="S2.p1.9.m9.2.2.2.2" xref="S2.p1.9.m9.2.2.2.2.cmml">0</mn></mrow></msub></mpadded><mo id="S2.p1.9.m9.2.3.3" xref="S2.p1.9.m9.2.3.3.cmml">=</mo><mrow id="S2.p1.9.m9.2.3.4" xref="S2.p1.9.m9.2.3.4.cmml"><mrow id="S2.p1.9.m9.2.3.4.2" xref="S2.p1.9.m9.2.3.4.2.cmml"><msub id="S2.p1.9.m9.2.3.4.2.2" xref="S2.p1.9.m9.2.3.4.2.2.cmml"><mi id="S2.p1.9.m9.2.3.4.2.2.2" xref="S2.p1.9.m9.2.3.4.2.2.2.cmml">R</mi><mn id="S2.p1.9.m9.2.3.4.2.2.3" xref="S2.p1.9.m9.2.3.4.2.2.3.cmml">0</mn></msub><mo id="S2.p1.9.m9.2.3.4.2.1" xref="S2.p1.9.m9.2.3.4.2.1.cmml">/</mo><mn id="S2.p1.9.m9.2.3.4.2.3" xref="S2.p1.9.m9.2.3.4.2.3.cmml">2</mn></mrow><mo id="S2.p1.9.m9.2.3.4.1" xref="S2.p1.9.m9.2.3.4.1.cmml">⁢</mo><msup id="S2.p1.9.m9.2.3.4.3" xref="S2.p1.9.m9.2.3.4.3.cmml"><mi id="S2.p1.9.m9.2.3.4.3.2" xref="S2.p1.9.m9.2.3.4.3.2.cmml">γ</mi><mn id="S2.p1.9.m9.2.3.4.3.3" xref="S2.p1.9.m9.2.3.4.3.3.cmml">2</mn></msup><mo id="S2.p1.9.m9.2.3.4.1a" xref="S2.p1.9.m9.2.3.4.1.cmml">⁢</mo><mi id="S2.p1.9.m9.2.3.4.4" xref="S2.p1.9.m9.2.3.4.4.cmml">c</mi></mrow><mo id="S2.p1.9.m9.2.3.5" xref="S2.p1.9.m9.2.3.5.cmml">≃</mo><mrow id="S2.p1.9.m9.2.3.6" xref="S2.p1.9.m9.2.3.6.cmml"><mpadded width="+1.7pt" id="S2.p1.9.m9.2.3.6.2" xref="S2.p1.9.m9.2.3.6.2.cmml"><mn id="S2.p1.9.m9.2.3.6.2a" xref="S2.p1.9.m9.2.3.6.2.cmml">1</mn></mpadded><mo id="S2.p1.9.m9.2.3.6.1" xref="S2.p1.9.m9.2.3.6.1.cmml">⁢</mo><mi id="S2.p1.9.m9.2.3.6.3" xref="S2.p1.9.m9.2.3.6.3.cmml">hour</mi></mrow></mrow></math>, <math><mrow id="S2.p1.10.m10.1.1" xref="S2.p1.10.m10.1.1.cmml"><mrow id="S2.p1.10.m10.1.1.2" xref="S2.p1.10.m10.1.1.2.cmml"><mi mathvariant="normal" id="S2.p1.10.m10.1.1.2.2" xref="S2.p1.10.m10.1.1.2.2.cmml">Δ</mi><mo id="S2.p1.10.m10.1.1.2.1" xref="S2.p1.10.m10.1.1.2.1.cmml">⁢</mo><mpadded width="+1.7pt" id="S2.p1.10.m10.1.1.2.3" xref="S2.p1.10.m10.1.1.2.3.cmml"><mi id="S2.p1.10.m10.1.1.2.3a" xref="S2.p1.10.m10.1.1.2.3.cmml">R</mi></mpadded></mrow><mo rspace="4.2pt" id="S2.p1.10.m10.1.1.3" xref="S2.p1.10.m10.1.1.3.cmml">≃</mo><mrow id="S2.p1.10.m10.1.1.4" xref="S2.p1.10.m10.1.1.4.cmml"><msub id="S2.p1.10.m10.1.1.4.2" xref="S2.p1.10.m10.1.1.4.2.cmml"><mi id="S2.p1.10.m10.1.1.4.2.2" xref="S2.p1.10.m10.1.1.4.2.2.cmml">R</mi><mn id="S2.p1.10.m10.1.1.4.2.3" xref="S2.p1.10.m10.1.1.4.2.3.cmml">0</mn></msub><mo id="S2.p1.10.m10.1.1.4.1" xref="S2.p1.10.m10.1.1.4.1.cmml">/</mo><msup id="S2.p1.10.m10.1.1.4.3" xref="S2.p1.10.m10.1.1.4.3.cmml"><mi id="S2.p1.10.m10.1.1.4.3.2" xref="S2.p1.10.m10.1.1.4.3.2.cmml">γ</mi><mn id="S2.p1.10.m10.1.1.4.3.3" xref="S2.p1.10.m10.1.1.4.3.3.cmml">2</mn></msup></mrow><mo id="S2.p1.10.m10.1.1.5" xref="S2.p1.10.m10.1.1.5.cmml">=</mo><mrow id="S2.p1.10.m10.1.1.6" xref="S2.p1.10.m10.1.1.6.cmml"><mrow id="S2.p1.10.m10.1.1.6.2" xref="S2.p1.10.m10.1.1.6.2.cmml"><mn id="S2.p1.10.m10.1.1.6.2.2" xref="S2.p1.10.m10.1.1.6.2.2.cmml">8.5</mn><mo id="S2.p1.10.m10.1.1.6.2.1" xref="S2.p1.10.m10.1.1.6.2.1.cmml">×</mo><msup id="S2.p1.10.m10.1.1.6.2.3" xref="S2.p1.10.m10.1.1.6.2.3.cmml"><mn id="S2.p1.10.m10.1.1.6.2.3.2" xref="S2.p1.10.m10.1.1.6.2.3.2.cmml">10</mn><mrow id="S2.p1.10.m10.1.1.6.2.3.3" xref="S2.p1.10.m10.1.1.6.2.3.3.cmml"><mo id="S2.p1.10.m10.1.1.6.2.3.3.1" xref="S2.p1.10.m10.1.1.6.2.3.3.1.cmml">-</mo><mn id="S2.p1.10.m10.1.1.6.2.3.3.2" xref="S2.p1.10.m10.1.1.6.2.3.3.2.cmml">5</mn></mrow></msup></mrow><mo id="S2.p1.10.m10.1.1.6.1" xref="S2.p1.10.m10.1.1.6.1.cmml">⁢</mo><mi id="S2.p1.10.m10.1.1.6.3" xref="S2.p1.10.m10.1.1.6.3.cmml">pc</mi></mrow></mrow></math>, <math><mrow id="S2.p1.11.m11.2.2" xref="S2.p1.11.m11.2.2.cmml"><mrow id="S2.p1.11.m11.2.2.1.1" xref="S2.p1.11.m11.2.2.1.2.cmml"><mo id="S2.p1.11.m11.2.2.1.1.2" xref="S2.p1.11.m11.2.2.1.2.cmml">[</mo><mrow id="S2.p1.11.m11.2.2.1.1.1" xref="S2.p1.11.m11.2.2.1.1.1.cmml"><mn id="S2.p1.11.m11.2.2.1.1.1.2" xref="S2.p1.11.m11.2.2.1.1.1.2.cmml">1.57</mn><mo id="S2.p1.11.m11.2.2.1.1.1.1" xref="S2.p1.11.m11.2.2.1.1.1.1.cmml">×</mo><msup id="S2.p1.11.m11.2.2.1.1.1.3" xref="S2.p1.11.m11.2.2.1.1.1.3.cmml"><mn id="S2.p1.11.m11.2.2.1.1.1.3.2" xref="S2.p1.11.m11.2.2.1.1.1.3.2.cmml">10</mn><mrow id="S2.p1.11.m11.2.2.1.1.1.3.3" xref="S2.p1.11.m11.2.2.1.1.1.3.3.cmml"><mo id="S2.p1.11.m11.2.2.1.1.1.3.3.1" xref="S2.p1.11.m11.2.2.1.1.1.3.3.1.cmml">-</mo><mn id="S2.p1.11.m11.2.2.1.1.1.3.3.2" xref="S2.p1.11.m11.2.2.1.1.1.3.3.2.cmml">2</mn></mrow></msup></mrow><mo id="S2.p1.11.m11.2.2.1.1.3" xref="S2.p1.11.m11.2.2.1.2.cmml">,</mo><mn id="S2.p1.11.m11.1.1" xref="S2.p1.11.m11.1.1.cmml"> 1.57</mn><mo rspace="5.3pt" id="S2.p1.11.m11.2.2.1.1.4" xref="S2.p1.11.m11.2.2.1.2.cmml">]</mo></mrow><mo id="S2.p1.11.m11.2.2.2" xref="S2.p1.11.m11.2.2.2.cmml">⁢</mo><mi id="S2.p1.11.m11.2.2.3" xref="S2.p1.11.m11.2.2.3.cmml">pc</mi></mrow></math>

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1006.3990

Formulas:

1-

2 θ \sim 51^{o}

2-

I (t_{j})

3-

(d) - (g)

4-

I (t_{j}) - I (off)

5-

I (t_{j})

6-

I_{1} (𝐐) \propto \sum_{j} \frac{1}{ω_{j} (𝐪)} (n_{j} (𝐪) + \frac{1}{2}) {| F_{j} (𝐐) |}^{2},

7-

ω_{j} (𝐪)

8-

n_{j} (𝐪)

9-

F_{j} (𝐐)

10-

F_{j} (𝐐) = \sum_{s} \frac{f_{s}}{\sqrt{m_{s}}} e^{- M_{s}} (𝐐 \cdot {\hat{𝐞}}_{s, j, 𝐪}) e^{- i 𝐊_{Q} \cdot 𝐫_{s}} .

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0805.0781

Formulas:

1-

ℒ = \bar{ψ} [i (γ^{μ} + c^{ν μ} γ_{ν} - d^{ν μ} γ_{ν} γ_{5}) \partial_{μ} - m] ψ .

2-

p^{+} \to n + π^{+}

3-

E_{w} (\vec{p}) = \sqrt{m_{w}^{2} + [1 + 2 δ_{w} (\hat{p})] {\vec{p}}^{2}},

4-

1 + δ_{w} (\hat{p})

5-

δ_{w} (\hat{p}) = - c_{00}^{w} - c_{(0 j)}^{w} {\hat{p}}_{j} - c_{j k}^{w} {\hat{p}}_{j} {\hat{p}}_{k} + s d_{00}^{w} + s d_{(0 j)}^{w} {\hat{p}}_{j} + s d_{j k}^{w} {\hat{p}}_{j} {\hat{p}}_{k},

6-

c_{(0 j)} = c_{0 j} + c_{j 0}

7-

d_{(0 j)}

8-

δ_{p} (\hat{p}) - δ_{w} (\hat{p})

9-

p^{+} \to p^{+} + γ

10-

p^{+} \to p^{+} + π^{0}

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/9411011

Formulas:

1-

Ψ (𝐫, 𝐤_{⟂}) = \exp (i 𝐤_{⟂} \cdot 𝐫_{⟂}) ϕ (x)

2-

E (𝐤_{⟂}) = E + (ℏ^{2} 𝐤_{⟂}^{2} / 2 m^{*})

3-

m_{l}^{*} / m_{t}^{*} \sim 5

4-

[- \frac{ℏ^{2}}{2 m^{*}} \frac{d^{2}}{d x^{2}} + V_{T F} (x) - e F x] ϕ (x) = E ϕ (x) .

5-

V_{T F} (z)

6-

τ (E, V)

7-

V_{T F} (z)

8-

τ (E, 0)

9-

j (V) = \frac{m^{*} e k_{B} T}{2 π^{2} ℏ^{3}} \int_{0}^{\infty} τ (E, V) N (E, V) 𝑑 E,

10-

N (E, V)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1205.5210

Formulas:

1-

| u_{ε} (x) - u_{0} (x) | \leq C_{κ} ε^{(d - 1) / 2} \frac{1}{d {(x)}^{κ}}

2-

\forall κ > d - 1

3-

{∥ u_{ε} - u_{0} ∥}_{L^{p}} \leq C_{κ} ε^{κ}

4-

\forall κ \in (0, 1 / 2 p)

5-

g (x / ε)

6-

u_{ε} (x) = \int_{\partial D} P (x, y) g (y / ε) 𝑑 σ (y),

7-

P (x, y) = n (y) A (y) \nabla G (x, y)

8-

| \partial D | \bar{g}

9-

A (x / ϵ)

10-

{|| u_{ε} - u_{0} ||}_{L^{2} (D)} \leq C_{α} ε^{κ}, \forall κ < (d - 1) / (3 d + 5) .

Formulas (html):

Correct Categorie: math

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1102.2826

Formulas:

1-

(\partial / \partial t) | 𝐔 ⟩ = - (ı / ℏ) H_{𝐔} | 𝐔 ⟩

2-

ℋ_{𝐒} \otimes ℋ_{𝐄} = ℋ_{𝐔}

3-

ℋ_{𝐒} \otimes ℋ_{𝐄} = ℋ_{𝐔}

4-

ℋ_{𝐒} \otimes ℋ_{𝐄} = ℋ_{𝐔}

5-

ℋ_{𝐒} \otimes ℋ_{𝐄} = ℋ_{𝐔}

6-

ℋ_{𝐒} \otimes ℋ_{𝐄_{k}} \otimes ℋ_{𝐎_{k}} = ℋ_{𝐔}

7-

ℋ_{𝐒} \otimes ℋ_{𝐄_{j}} \otimes ℋ_{𝐎_{j}} = ℋ_{𝐒} \otimes ℋ_{𝐄_{k}} \otimes ℋ_{𝐎_{k}} = ℋ_{𝐔}

8-

H_{𝐔} = \sum_{𝑖𝑗} H_{𝑖𝑗}

9-

⟨ s_{j} | H_{𝐒 - 𝐄} | e_{k} ⟩

10-

| 𝐒 (t_{0}) ⟩

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/9901165

Formulas:

1-

u_{e x t}^{'}

2-

u_{e x t}^{'} = Γ^{2} u_{e x t}

3-

{\dot{γ}}_{a c c}

4-

γ_{b} \propto {\dot{γ}}_{a c c}^{1 / 2} u_{e x t}^{- 1 / 2} Γ^{- 1}

5-

δ = {(Γ [1 - β_{Γ} \cos θ])}^{- 1} \approx Γ

6-

ϵ_{s y} \propto B^{'} γ_{b}^{2} Γ \propto {\dot{γ}}_{a c c} B^{'} u_{e x t}^{- 1} Γ^{- 1},

7-

L_{s y} \propto B^{'}^{2} Γ^{4} γ_{b}^{2} \propto {\dot{γ}}_{a c c} B^{'}^{2} Γ^{2} u_{e x t}^{- 1} .

8-

B^{'} \propto {\dot{γ}}_{a c c}^{1 / 4} u_{e x t}^{- 1 / 4} Γ^{- 1 / 2}

9-

ϵ_{s y}^{e p} \propto {\dot{γ}}_{a c c}^{5 / 4} u_{e x t}^{- 5 / 4} Γ^{- 3 / 2}

10-

L_{s y}^{e p} \propto {\dot{γ}}_{a c c}^{3 / 2} u_{e x t}^{- 3 / 2} Γ .

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/quant-ph/0103008

Formulas:

1-

ℋ = g_{e} μ_{B} B_{0} S_{z} + g_{n} μ_{n} B_{0} I_{z} - A \vec{S} \vec{I},

2-

S = I = 1 / 2

3-

A / 2 π ℏ \approx 3.5

4-

f = f_{e 0} = g_{e} μ_{B} B_{0} / 2 π ℏ + A / 4 π ℏ .

5-

f = f_{e 1} = g_{e} μ_{B} B_{0} / 2 π ℏ - A / 4 π ℏ .

6-

A / 2 π ℏ

7-

Δ f_{e} = (g_{e} μ_{B} / 2 π ℏ) a \frac{\partial B_{0}}{\partial x} .

8-

Δ f_{n} = (g_{n} μ_{n} / 2 π ℏ) a \frac{\partial B_{0}}{\partial x} .

9-

\partial B_{0} / \partial x = 10^{5}

10-

Δ f_{n} \approx 6.75

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/1602.01316

Formulas:

1-

{(\frac{σ_{A}}{A})}^{2} = (f^{2} + (F a n o)) / n_{p r i m a r y} + σ_{i n s t r u m e n t a l}^{2}

2-

n_{p r i m a r y}

3-

σ_{N}^{2} = \bar{N^{2}} - {\bar{N}}^{2}

4-

f = σ_{N} / \bar{N}

5-

E_{d r i f t}

6-

f_{a l l}

7-

f_{α} = \sqrt{\bar{α^{2}} - {\bar{α}}^{2}} / \bar{α} = σ_{α} / \bar{α}

8-

(α * α) (k) = \sum_{m = 0}^{k} α (m) α (k - m)

9-

{(α)}^{l, *} (k)

10-

{(α)}^{(l + 1), *} (k) = \sum_{m = 0}^{k} (α^{l, *}) (m) α (k - m)

Formulas (html):

Correct Categorie: physics

Guessed Categorie: quant-ph

Result: incorrect

Run 11332270 (Agent494)