Run 11332253

Paper: https://arxiv.org/abs/astro-ph/9710204

Formulas:

1-

ξ_{n} = Q_{n} ξ_{2}^{n - 1}

2-

j = 0, \dots, J

3-

l = 0, \dots, 2^{j} - 1

4-

\bar{ρ} = M_{0} / L

5-

ϵ (x) \equiv (ρ (x) - \bar{ρ}) / \bar{ρ}

6-

ϵ_{0, 0} = 0 + \tilde{ϵ}

7-

ϵ_{j + 1, 2 l}

8-

ϵ_{j, l} + {\tilde{ϵ}}_{j, l}

9-

ϵ_{j + 1, 2 l + 1}

10-

ϵ_{j, l} - {\tilde{ϵ}}_{j, l}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/hep-th/9604110

Formulas:

1-

S = \int d^{3} ζ (\frac{1}{2} \sqrt{- g} g^{i j} E_{i}^{a} E_{j}^{b} η_{a b} - \frac{1}{6} ϵ^{i j k} E_{i}^{A} E_{j}^{B} E_{k}^{C} A_{C B A} - \frac{1}{2} \sqrt{- g}) .

2-

A_{C B A}

3-

S = \int d^{3} ζ (\frac{1}{2} \sqrt{- g} g^{i j} \partial_{i} x^{m} \partial_{j} x^{n} G_{m n} - \frac{1}{6} ϵ^{i j k} \partial_{i} x^{m} \partial_{j} x^{n} \partial_{k} x^{p} A_{p n m} - \frac{1}{2} \sqrt{- g}) .

4-

x^{m}, m = 1, \dots, 11

5-

x^{I} = x^{I} + 2 π R^{I}, I = 10, 11

6-

R^{11} R^{10} = 2 .

7-

z^{i} i = 1, 2

8-

g^{i j} = ϕ^{- 2 / 3} (\begin{matrix} {\hat{g}}^{i j} + ϕ V_{i} V_{j} & ϕ^{2} V_{i} \\ ϕ^{2} V_{j} & ϕ^{2} \end{matrix}) .

9-

S = \int d^{2} z \sqrt{- \hat{g}} {\hat{g}}^{i j} \partial_{i} {\hat{x}}^{m} \partial_{j} {\hat{x}}^{n} {\hat{G}}_{m n} + \frac{1}{2} ϵ^{i j} \partial_{i} {\hat{x}}^{m} \partial_{j} {\hat{x}}^{n} {\hat{A}}_{n m}, i, j = 1, 2 .

10-

{\hat{x}}^{m}, m = 1, \dots, 10

Formulas (html):

Correct Categorie: hep-th

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/9709136

Formulas:

1-

< z > = 0.2648 \pm 0.0002

2-

163 \pm 57 km s^{- 1}

3-

< z > = 0.2643 \pm 0.0004

4-

223 \pm 91 km s^{- 1}

5-

\sim 1060 km s^{- 1}

6-

< z > = 0.0901 \pm 0.0007

7-

530 \pm 200 km s^{- 1}

8-

\sim 427 km s^{- 1}

9-

< z > = 0.2648 \pm 0.0002

10-

163 \pm 57 km s^{- 1}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1909.08561

Formulas:

1-

{B (x, y) : x, y \in L}

2-

Q (v) = B (v, v)

3-

L ≅ ⟨ a_{1}, \dots, a_{n} ⟩

4-

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

5-

Q (L) = {Q (v) : v \in L}

6-

a \in Q (L)

7-

Q (v) > 0

8-

ℕ ∖ Q (L)

9-

α_{0} \in ℤ_{p}^{\times}

10-

α = p^{{ord}_{p} α} α_{0}

Formulas (html):

Correct Categorie: math

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1504.02143

Formulas:

1-

w < ⟨ k ⟩ p - r

2-

P_{A} (k)

3-

A \in {S, I}

4-

P_{S, I} (k)

5-

{\hat{P}}_{A} (k) \equiv [A] P_{A} (k)

6-

f_{A} = \frac{[S I]}{[A] ⟨ k_{A} ⟩}

7-

\frac{d {\hat{P}}_{I} (k)}{d t} =

8-

p f_{S} k {\hat{P}}_{S} (k) - r {\hat{P}}_{I} (k)

9-

+ w f_{I} [(k + 1) {\hat{P}}_{I} (k + 1) - k {\hat{P}}_{I} (k)]

10-

\frac{d {\hat{P}}_{S} (k)}{d t} =

Formulas (html):

Correct Categorie: nlin

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0511589

Formulas:

1-

ν F_{ν} \propto ν^{n}

2-

3 \times 10^{- 2} M_{⊙}

3-

3 \times 10^{- 3} M_{⊙}

4-

6 \times 10^{- 4} M_{⊙}

5-

3, 5, 7 \times σ

6-

2.4 \times 10^{- 2} M_{⊙}

7-

\sim 10^{- 7} M_{⊙}

8-

Σ \sim r^{- 3 / 2}

9-

8 \times 10^{- 4} M_{⊙}

10-

8 \times 10^{- 6} M_{⊙} ≃ 3 M_{\oplus}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1112.5974

Formulas:

1-

μ_{0} H_{P} \sim

2-

C (H) / T

3-

C (H) / T

4-

δ ω (𝒓, 𝒌) \propto 𝒗_{s} (𝒓) \cdot 𝒗_{F} (𝒌)

5-

𝒗_{s} (𝒓)

6-

𝒗_{F} (𝒌)

7-

δ ω^{node} \propto 𝒗_{s} \cdot 𝒗_{F}^{node}

8-

𝒗_{F}^{node} \equiv 𝒗_{F} (𝒌_{F}^{node})

9-

𝒗_{s} ⟂ 𝒗_{F}^{node}

10-

C (ϕ) / T

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/hep-lat/0609022

Formulas:

1-

ℒ = \frac{1}{2} ξ^{⊤} 𝒞 (\partial̸ + m) ξ - \frac{g^{2}}{8} {(ξ^{⊤} 𝒞 ξ)}^{2} .

2-

𝒞 γ_{μ} 𝒞^{- 1} = - γ_{μ}^{⊤}

3-

ξ \to γ_{5} ξ

4-

\partial_{μ} \to {\tilde{\partial}}_{μ}, m \to m - \frac{a}{2} \partial_{μ} \partial_{μ}^{*}

5-

m = m_{c} (g^{2})

6-

ξ (x + T \hat{0}) = - ξ (x), ξ (x + L \hat{1}) = + ξ (x),

7-

p_{*} = (π / T, 0)

8-

\overset{˘}{ξ} (x_{0}, p) = a \sum_{x_{1}} e^{- i p x_{1}} ξ (x), \overset{˘}{ξ} (x_{0}) \equiv \overset{˘}{ξ} (x_{0}, 0)

9-

⟨ {\overset{˘}{ξ}}^{⊤} (T / 4) 𝒞 \overset{˘}{ξ} (0) ⟩,

10-

\frac{- 1}{N L} ⟨ {\overset{˘}{ξ}}^{⊤} (T / 2) 𝒞 γ_{0} \overset{˘}{ξ} (0) ⟩ .

Formulas (html):

Correct Categorie: hep-lat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1708.01737

Formulas:

1-

2 π / g_{2}

2-

H_{I} = g_{1} σ_{z} x

3-

H_{I} = g_{2} σ_{z} x^{2}

4-

H = H_{q} + H_{0} + H_{I} = \frac{1}{2} ω_{q} σ_{z} + \frac{1}{2} ω_{0} ({\hat{x}}^{2} + {\hat{p}}^{2}) + g_{1} σ_{z} \hat{x} + \frac{1}{2} g_{2} σ_{z} {\hat{x}}^{2} .

5-

\hat{x} \to \frac{\hat{x}}{m ω_{0}}

6-

\hat{p} \to \hat{p} m ω_{0}

7-

| ψ (0) ⟩ = (| 0 ⟩ + | 1 ⟩) / \sqrt{2}

8-

ρ_{0} = \frac{1}{Z} e^{- β H_{0}}

9-

Z = 1 / (2 \sinh \frac{β ω_{0}}{2})

10-

β = 1 / k_{B} T

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/1902.04670

Formulas:

1-

B (z) = B (z_{0}) (\frac{z_{0}}{z}),

2-

B_{0} = B (z_{0})

3-

\frac{B^{2} (z_{0})}{8 π} = \frac{L_{jet}}{π r_{0}^{2} v_{jet}},

4-

n_{p} (z) ≃ \frac{{\dot{m}}_{j}}{π {[R_{j} (z)]}^{2} m_{p} v_{j}} .

5-

z_{0} = 100 r_{g}

6-

z_{acc} = 300 r_{g}

7-

L_{rel} = q_{rel} L_{jet},

8-

L_{rel} = L_{p} + L_{e}

9-

L_{p} = a L_{e} a = 100 .

10-

Q^{'} (E^{'}, z^{'}) = Q_{0} \frac{E^{'}^{- p}}{z^{'}} [Q^{'}] = {erg}^{- 1} s^{- 1} {cm}^{- 3},

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1908.05127

Formulas:

1-

{𝖤𝗇𝖼}_{g, h} (m) = [a, b]

2-

{𝖣𝖾𝖼}_{g, x} (a, b) = m

3-

[a_{1}, b_{1}] := {𝖤𝗇𝖼}_{g_{1}, h_{1}} (m)

4-

[a_{2}, b_{2}] := {𝖤𝗇𝖼}_{g_{2}, h_{2}} (a_{1})

5-

[a_{3}, b_{3}] := {𝖤𝗇𝖼}_{g_{3}, h_{3}} (a_{2})

6-

[b_{1}, b_{2}, a_{3}, b_{3}]

7-

a_{2} := {𝖣𝖾𝖼}_{g_{3}, x_{3}} (a_{3}, b_{3})

8-

a_{1} := {𝖣𝖾𝖼}_{g_{2}, x_{2}} (a_{2}, b_{2})

9-

m := {𝖣𝖾𝖼}_{g_{1}, x_{1}} (a_{1}, b_{1})

10-

G F (p)

Formulas (html):

Correct Categorie: cs

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0604461

Formulas:

1-

v \sim h^{3 / 2}

2-

\dot{γ} \sim \sqrt{\sin (β - β_{s})}

3-

β - β_{s} \sim Ω

4-

\sin (β - β_{s}) ≃ β - β_{s}

5-

Q = π Ω (R^{2} - h^{2})

6-

Q = π Ω R^{2}

7-

m = (1 - n) / n

8-

d = 2 m m

9-

100 < D / d < 400

10-

ω^{2} R / g

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/hep-ex/0111015

Formulas:

1-

δ 1 / p \sim 4 \cdot 10^{- 5} / GeV

2-

e^{+} e^{-} \to ZH, Z \to ℓ^{+} ℓ^{-}

3-

Δ E / E \approx 30 % / \sqrt{E}

4-

H \to b \bar{b}, H \to c \bar{c}

5-

3 \times 3 {cm}^{2}

6-

5 \times 5 {cm}^{2}

7-

25 \times 25 {cm}^{2}

8-

1 \times 1 {cm}^{2}

9-

Δ \frac{1}{p} \approx 4 \cdot 10^{- 5} / GeV

10-

e^{+} e^{-} \to ZH, Z \to μ^{+} μ^{-}

Formulas (html):

Correct Categorie: hep-ex

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1304.7833

Formulas:

1-

𝒪 (n \log n)

2-

Θ (n^{2})

3-

𝒪 (n \log^{2} n)

4-

𝒪 (n \log n)

5-

Ω (n \log n)

6-

𝒪 (n \log n)

7-

𝒪 (n \log^{2} n)

8-

𝒪 (n \log n)

9-

q_{i}, q_{j} \in ℝ^{n}

10-

(i_{1}, i_{2}, \dots, i_{n})

Formulas (html):

Correct Categorie: cs

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/hep-th/0105150

Formulas:

1-

C^{\infty} (𝐑^{n}, U (1))

2-

C^{\infty} (𝐑^{n}, U (1))

3-

e^{- S [ϕ]} \prod_{x} d ϕ (x)

4-

e^{- S [ϕ]}

5-

\prod_{x} d ϕ (x)

6-

\prod_{x} d ω (x)

7-

d ω (x)

8-

C^{\infty} (𝐑^{n}, U (1))

9-

C^{\infty} (𝐑^{n}, U (1))

10-

f \in C^{\infty} (𝐑)

Formulas (html):

Correct Categorie: hep-th

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0210590

Formulas:

1-

T = 80^{o} C

2-

L = 2 l + D

3-

L = 2 l + D_{0} ω^{- 1}, D_{0} \equiv 2 π (χ^{1 / 6} n_{0}^{- 1 / 3}) b \sim b

4-

c (n) = 1

5-

c (n) = 0

6-

S = T \int_{0}^{N} L (c (n), \dot{c} (n)) d n, R = \frac{Θ}{2} \int_{0}^{N} {(\dot{c} (n))}^{2} d n

7-

L = K - Π; K \equiv \frac{m}{2} {(\dot{c} (n))}^{2}, Π \equiv \frac{τ}{2} {(c (n))}^{2} .

8-

\bar{{(m - \bar{m})}^{2}} \equiv σ^{2}

9-

\exp (- S / T)

10-

K = \frac{1}{2} (\bar{m} - \tilde{Δ}) {(\dot{c} (n))}^{2}, \tilde{Δ} \equiv \frac{σ^{2}}{2} \int_{0}^{N} {(\dot{c} (n^{'}))}^{2} d n^{'} .

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1610.07324

Formulas:

1-

s c a l e = r a d i u s__{l i d a r} / r a d i u s__{S F M}

2-

r a d i u s__{l i d a r}

3-

r a d i u s__{S F M}

4-

r a d i u s__{S F M}

5-

r a d i u s__{l i d a r}

6-

P_{S F M} = P_{S F M} * s c a l e

7-

P_{S F M}

8-

S i m i__{m a t c h i n g}

9-

S i m i__{m a t c h i n g} = {∥ E S F__{l i d a r} - E S F__{S F M} ∥}_{F}

10-

E S F__{l i d a r}

Formulas (html):

Correct Categorie: cs

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1408.1492

Formulas:

1-

[α_{i}, β_{i}]

2-

D_{i} (t, x)

3-

x = x_{i, t - 1}

4-

D_{i} (t, x)

5-

d_{i} (t, x)

6-

D_{i} (t, x)

7-

d_{i} (t, x)

8-

x + \min (c, d_{i} (t, x)) \geq x^{'} + \min (c, d_{i} (t, x^{'})) .

9-

d_{i} (t, x) = k

10-

d_{i} (t, x) = g (t)

Formulas (html):

Correct Categorie: cs

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/9606066

Formulas:

1-

p_{aval} (s) \propto s^{- τ} .

2-

1 < τ \leq \frac{3}{2}

3-

0 \leq x_{i} < 1

4-

p_{stress} (η)

5-

p_{stress} (η)

6-

p_{stress} (η) = \frac{1}{σ} \exp (- η / σ) .

7-

p (η) \propto e x p (- {(η / σ)}^{q})

8-

p_{thresh} (x)

9-

p_{thresh} (x)

10-

P_{move} (x) = \int_{x}^{\infty} p_{stress} (η) d η = e^{- x / σ} .

Formulas (html):

<math><mrow id="S1.E1.m1.2.2.1" xref="S1.E1.m1.2.2.1.1.cmml"><mrow id="S1.E1.m1.2.2.1.1" xref="S1.E1.m1.2.2.1.1.cmml"><mrow id="S1.E1.m1.2.2.1.1.2" xref="S1.E1.m1.2.2.1.1.2.cmml"><msub id="S1.E1.m1.2.2.1.1.2.2" xref="S1.E1.m1.2.2.1.1.2.2.cmml"><mi id="S1.E1.m1.2.2.1.1.2.2.2" xref="S1.E1.m1.2.2.1.1.2.2.2.cmml">p</mi><mi id="S1.E1.m1.2.2.1.1.2.2.3" xref="S1.E1.m1.2.2.1.1.2.2.3.cmml">aval</mi></msub><mo id="S1.E1.m1.2.2.1.1.2.1" xref="S1.E1.m1.2.2.1.1.2.1.cmml">⁢</mo><mrow id="S1.E1.m1.2.2.1.1.2.3.2" xref="S1.E1.m1.2.2.1.1.2.cmml"><mo stretchy="false" id="S1.E1.m1.2.2.1.1.2.3.2.1" xref="S1.E1.m1.2.2.1.1.2.cmml">(</mo><mi id="S1.E1.m1.1.1" xref="S1.E1.m1.1.1.cmml">s</mi><mo stretchy="false" id="S1.E1.m1.2.2.1.1.2.3.2.2" xref="S1.E1.m1.2.2.1.1.2.cmml">)</mo></mrow></mrow><mo id="S1.E1.m1.2.2.1.1.1" xref="S1.E1.m1.2.2.1.1.1.cmml">∝</mo><msup id="S1.E1.m1.2.2.1.1.3" xref="S1.E1.m1.2.2.1.1.3.cmml"><mi id="S1.E1.m1.2.2.1.1.3.2" xref="S1.E1.m1.2.2.1.1.3.2.cmml">s</mi><mrow id="S1.E1.m1.2.2.1.1.3.3" xref="S1.E1.m1.2.2.1.1.3.3.cmml"><mo id="S1.E1.m1.2.2.1.1.3.3.1" xref="S1.E1.m1.2.2.1.1.3.3.1.cmml">-</mo><mi id="S1.E1.m1.2.2.1.1.3.3.2" xref="S1.E1.m1.2.2.1.1.3.3.2.cmml">τ</mi></mrow></msup></mrow><mo id="S1.E1.m1.2.2.1.2" xref="S1.E1.m1.2.2.1.1.cmml">.</mo></mrow></math>, <math><mrow id="S1.p2.3.m2.1.1" xref="S1.p2.3.m2.1.1.cmml"><mn id="S1.p2.3.m2.1.1.2" xref="S1.p2.3.m2.1.1.2.cmml">1</mn><mo id="S1.p2.3.m2.1.1.3" xref="S1.p2.3.m2.1.1.3.cmml"><</mo><mi id="S1.p2.3.m2.1.1.4" xref="S1.p2.3.m2.1.1.4.cmml">τ</mi><mo id="S1.p2.3.m2.1.1.5" xref="S1.p2.3.m2.1.1.5.cmml">≤</mo><mfrac id="S1.p2.3.m2.1.1.6" xref="S1.p2.3.m2.1.1.6.cmml"><mn id="S1.p2.3.m2.1.1.6.2" xref="S1.p2.3.m2.1.1.6.2.cmml">3</mn><mn id="S1.p2.3.m2.1.1.6.3" xref="S1.p2.3.m2.1.1.6.3.cmml">2</mn></mfrac></mrow></math>, <math><mrow id="S1.p3.7.m7.1.1" xref="S1.p3.7.m7.1.1.cmml"><mn id="S1.p3.7.m7.1.1.2" xref="S1.p3.7.m7.1.1.2.cmml">0</mn><mo id="S1.p3.7.m7.1.1.3" xref="S1.p3.7.m7.1.1.3.cmml">≤</mo><msub id="S1.p3.7.m7.1.1.4" xref="S1.p3.7.m7.1.1.4.cmml"><mi id="S1.p3.7.m7.1.1.4.2" xref="S1.p3.7.m7.1.1.4.2.cmml">x</mi><mi id="S1.p3.7.m7.1.1.4.3" xref="S1.p3.7.m7.1.1.4.3.cmml">i</mi></msub><mo id="S1.p3.7.m7.1.1.5" xref="S1.p3.7.m7.1.1.5.cmml"><</mo><mn id="S1.p3.7.m7.1.1.6" xref="S1.p3.7.m7.1.1.6.cmml">1</mn></mrow></math>, <math><mrow id="S1.I1.i2.p1.2.m2.1.2" xref="S1.I1.i2.p1.2.m2.1.2.cmml"><msub id="S1.I1.i2.p1.2.m2.1.2.2" xref="S1.I1.i2.p1.2.m2.1.2.2.cmml"><mi id="S1.I1.i2.p1.2.m2.1.2.2.2" xref="S1.I1.i2.p1.2.m2.1.2.2.2.cmml">p</mi><mi id="S1.I1.i2.p1.2.m2.1.2.2.3" xref="S1.I1.i2.p1.2.m2.1.2.2.3.cmml">stress</mi></msub><mo id="S1.I1.i2.p1.2.m2.1.2.1" xref="S1.I1.i2.p1.2.m2.1.2.1.cmml">⁢</mo><mrow id="S1.I1.i2.p1.2.m2.1.2.3.2" xref="S1.I1.i2.p1.2.m2.1.2.cmml"><mo stretchy="false" id="S1.I1.i2.p1.2.m2.1.2.3.2.1" xref="S1.I1.i2.p1.2.m2.1.2.cmml">(</mo><mi id="S1.I1.i2.p1.2.m2.1.1" xref="S1.I1.i2.p1.2.m2.1.1.cmml">η</mi><mo stretchy="false" id="S1.I1.i2.p1.2.m2.1.2.3.2.2" xref="S1.I1.i2.p1.2.m2.1.2.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S1.p4.2.m2.1.2" xref="S1.p4.2.m2.1.2.cmml"><msub id="S1.p4.2.m2.1.2.2" xref="S1.p4.2.m2.1.2.2.cmml"><mi id="S1.p4.2.m2.1.2.2.2" xref="S1.p4.2.m2.1.2.2.2.cmml">p</mi><mi id="S1.p4.2.m2.1.2.2.3" xref="S1.p4.2.m2.1.2.2.3.cmml">stress</mi></msub><mo id="S1.p4.2.m2.1.2.1" xref="S1.p4.2.m2.1.2.1.cmml">⁢</mo><mrow id="S1.p4.2.m2.1.2.3.2" xref="S1.p4.2.m2.1.2.cmml"><mo stretchy="false" id="S1.p4.2.m2.1.2.3.2.1" xref="S1.p4.2.m2.1.2.cmml">(</mo><mi id="S1.p4.2.m2.1.1" xref="S1.p4.2.m2.1.1.cmml">η</mi><mo stretchy="false" id="S1.p4.2.m2.1.2.3.2.2" xref="S1.p4.2.m2.1.2.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S2.E2.m1.3.3.1" xref="S2.E2.m1.3.3.1.1.cmml"><mrow id="S2.E2.m1.3.3.1.1" xref="S2.E2.m1.3.3.1.1.cmml"><mrow id="S2.E2.m1.3.3.1.1.3" xref="S2.E2.m1.3.3.1.1.3.cmml"><msub id="S2.E2.m1.3.3.1.1.3.2" xref="S2.E2.m1.3.3.1.1.3.2.cmml"><mi id="S2.E2.m1.3.3.1.1.3.2.2" xref="S2.E2.m1.3.3.1.1.3.2.2.cmml">p</mi><mi id="S2.E2.m1.3.3.1.1.3.2.3" xref="S2.E2.m1.3.3.1.1.3.2.3.cmml">stress</mi></msub><mo id="S2.E2.m1.3.3.1.1.3.1" xref="S2.E2.m1.3.3.1.1.3.1.cmml">⁢</mo><mrow id="S2.E2.m1.3.3.1.1.3.3.2" xref="S2.E2.m1.3.3.1.1.3.cmml"><mo stretchy="false" id="S2.E2.m1.3.3.1.1.3.3.2.1" xref="S2.E2.m1.3.3.1.1.3.cmml">(</mo><mi id="S2.E2.m1.1.1" xref="S2.E2.m1.1.1.cmml">η</mi><mo stretchy="false" id="S2.E2.m1.3.3.1.1.3.3.2.2" xref="S2.E2.m1.3.3.1.1.3.cmml">)</mo></mrow></mrow><mo id="S2.E2.m1.3.3.1.1.2" xref="S2.E2.m1.3.3.1.1.2.cmml">=</mo><mrow id="S2.E2.m1.3.3.1.1.1" xref="S2.E2.m1.3.3.1.1.1.cmml"><mfrac id="S2.E2.m1.3.3.1.1.1.3" xref="S2.E2.m1.3.3.1.1.1.3.cmml"><mn id="S2.E2.m1.3.3.1.1.1.3.2" xref="S2.E2.m1.3.3.1.1.1.3.2.cmml">1</mn><mi id="S2.E2.m1.3.3.1.1.1.3.3" xref="S2.E2.m1.3.3.1.1.1.3.3.cmml">σ</mi></mfrac><mo id="S2.E2.m1.3.3.1.1.1.2" xref="S2.E2.m1.3.3.1.1.1.2.cmml">⁢</mo><mrow id="S2.E2.m1.3.3.1.1.1.1.1" xref="S2.E2.m1.3.3.1.1.1.1.2.cmml"><mi id="S2.E2.m1.2.2" xref="S2.E2.m1.2.2.cmml">exp</mi><mo id="S2.E2.m1.3.3.1.1.1.1.1a" xref="S2.E2.m1.3.3.1.1.1.1.2.cmml">⁡</mo><mrow id="S2.E2.m1.3.3.1.1.1.1.1.1" xref="S2.E2.m1.3.3.1.1.1.1.2.cmml"><mo stretchy="false" id="S2.E2.m1.3.3.1.1.1.1.1.1.2" xref="S2.E2.m1.3.3.1.1.1.1.2.cmml">(</mo><mrow id="S2.E2.m1.3.3.1.1.1.1.1.1.1" xref="S2.E2.m1.3.3.1.1.1.1.1.1.1.cmml"><mo id="S2.E2.m1.3.3.1.1.1.1.1.1.1.1" xref="S2.E2.m1.3.3.1.1.1.1.1.1.1.1.cmml">-</mo><mrow id="S2.E2.m1.3.3.1.1.1.1.1.1.1.2" xref="S2.E2.m1.3.3.1.1.1.1.1.1.1.2.cmml"><mi id="S2.E2.m1.3.3.1.1.1.1.1.1.1.2.2" xref="S2.E2.m1.3.3.1.1.1.1.1.1.1.2.2.cmml">η</mi><mo id="S2.E2.m1.3.3.1.1.1.1.1.1.1.2.1" xref="S2.E2.m1.3.3.1.1.1.1.1.1.1.2.1.cmml">/</mo><mi id="S2.E2.m1.3.3.1.1.1.1.1.1.1.2.3" xref="S2.E2.m1.3.3.1.1.1.1.1.1.1.2.3.cmml">σ</mi></mrow></mrow><mo stretchy="false" id="S2.E2.m1.3.3.1.1.1.1.1.1.3" xref="S2.E2.m1.3.3.1.1.1.1.2.cmml">)</mo></mrow></mrow></mrow></mrow><mo id="S2.E2.m1.3.3.1.2" xref="S2.E2.m1.3.3.1.1.cmml">.</mo></mrow></math>, <math><mrow id="S2.p1.11.m10.2.2" xref="S2.p1.11.m10.2.2.cmml"><mrow id="S2.p1.11.m10.2.2.3" xref="S2.p1.11.m10.2.2.3.cmml"><mi id="S2.p1.11.m10.2.2.3.2" xref="S2.p1.11.m10.2.2.3.2.cmml">p</mi><mo id="S2.p1.11.m10.2.2.3.1" xref="S2.p1.11.m10.2.2.3.1.cmml">⁢</mo><mrow id="S2.p1.11.m10.2.2.3.3.2" xref="S2.p1.11.m10.2.2.3.cmml"><mo stretchy="false" id="S2.p1.11.m10.2.2.3.3.2.1" xref="S2.p1.11.m10.2.2.3.cmml">(</mo><mi id="S2.p1.11.m10.1.1" xref="S2.p1.11.m10.1.1.cmml">η</mi><mo stretchy="false" id="S2.p1.11.m10.2.2.3.3.2.2" xref="S2.p1.11.m10.2.2.3.cmml">)</mo></mrow></mrow><mo id="S2.p1.11.m10.2.2.2" xref="S2.p1.11.m10.2.2.2.cmml">∝</mo><mrow id="S2.p1.11.m10.2.2.1" xref="S2.p1.11.m10.2.2.1.cmml"><mi id="S2.p1.11.m10.2.2.1.3" xref="S2.p1.11.m10.2.2.1.3.cmml">e</mi><mo id="S2.p1.11.m10.2.2.1.2" xref="S2.p1.11.m10.2.2.1.2.cmml">⁢</mo><mi id="S2.p1.11.m10.2.2.1.4" xref="S2.p1.11.m10.2.2.1.4.cmml">x</mi><mo id="S2.p1.11.m10.2.2.1.2a" xref="S2.p1.11.m10.2.2.1.2.cmml">⁢</mo><mi id="S2.p1.11.m10.2.2.1.5" xref="S2.p1.11.m10.2.2.1.5.cmml">p</mi><mo id="S2.p1.11.m10.2.2.1.2b" xref="S2.p1.11.m10.2.2.1.2.cmml">⁢</mo><mrow id="S2.p1.11.m10.2.2.1.1.1" xref="S2.p1.11.m10.2.2.1.1.1.1.cmml"><mo stretchy="false" id="S2.p1.11.m10.2.2.1.1.1.2" xref="S2.p1.11.m10.2.2.1.1.1.1.cmml">(</mo><mrow id="S2.p1.11.m10.2.2.1.1.1.1" xref="S2.p1.11.m10.2.2.1.1.1.1.cmml"><mo id="S2.p1.11.m10.2.2.1.1.1.1.2" xref="S2.p1.11.m10.2.2.1.1.1.1.2.cmml">-</mo><msup id="S2.p1.11.m10.2.2.1.1.1.1.1" xref="S2.p1.11.m10.2.2.1.1.1.1.1.cmml"><mrow id="S2.p1.11.m10.2.2.1.1.1.1.1.1.1" xref="S2.p1.11.m10.2.2.1.1.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S2.p1.11.m10.2.2.1.1.1.1.1.1.1.2" xref="S2.p1.11.m10.2.2.1.1.1.1.1.1.1.1.cmml">(</mo><mrow id="S2.p1.11.m10.2.2.1.1.1.1.1.1.1.1" xref="S2.p1.11.m10.2.2.1.1.1.1.1.1.1.1.cmml"><mi id="S2.p1.11.m10.2.2.1.1.1.1.1.1.1.1.2" xref="S2.p1.11.m10.2.2.1.1.1.1.1.1.1.1.2.cmml">η</mi><mo id="S2.p1.11.m10.2.2.1.1.1.1.1.1.1.1.1" xref="S2.p1.11.m10.2.2.1.1.1.1.1.1.1.1.1.cmml">/</mo><mi id="S2.p1.11.m10.2.2.1.1.1.1.1.1.1.1.3" xref="S2.p1.11.m10.2.2.1.1.1.1.1.1.1.1.3.cmml">σ</mi></mrow><mo stretchy="false" id="S2.p1.11.m10.2.2.1.1.1.1.1.1.1.3" xref="S2.p1.11.m10.2.2.1.1.1.1.1.1.1.1.cmml">)</mo></mrow><mi id="S2.p1.11.m10.2.2.1.1.1.1.1.3" xref="S2.p1.11.m10.2.2.1.1.1.1.1.3.cmml">q</mi></msup></mrow><mo stretchy="false" id="S2.p1.11.m10.2.2.1.1.1.3" xref="S2.p1.11.m10.2.2.1.1.1.1.cmml">)</mo></mrow></mrow></mrow></math>, <math><mrow id="S2.p3.2.m2.1.2" xref="S2.p3.2.m2.1.2.cmml"><msub id="S2.p3.2.m2.1.2.2" xref="S2.p3.2.m2.1.2.2.cmml"><mi id="S2.p3.2.m2.1.2.2.2" xref="S2.p3.2.m2.1.2.2.2.cmml">p</mi><mi id="S2.p3.2.m2.1.2.2.3" xref="S2.p3.2.m2.1.2.2.3.cmml">thresh</mi></msub><mo id="S2.p3.2.m2.1.2.1" xref="S2.p3.2.m2.1.2.1.cmml">⁢</mo><mrow id="S2.p3.2.m2.1.2.3.2" xref="S2.p3.2.m2.1.2.cmml"><mo stretchy="false" id="S2.p3.2.m2.1.2.3.2.1" xref="S2.p3.2.m2.1.2.cmml">(</mo><mi id="S2.p3.2.m2.1.1" xref="S2.p3.2.m2.1.1.cmml">x</mi><mo stretchy="false" id="S2.p3.2.m2.1.2.3.2.2" xref="S2.p3.2.m2.1.2.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S2.p3.6.m6.1.2" xref="S2.p3.6.m6.1.2.cmml"><msub id="S2.p3.6.m6.1.2.2" xref="S2.p3.6.m6.1.2.2.cmml"><mi id="S2.p3.6.m6.1.2.2.2" xref="S2.p3.6.m6.1.2.2.2.cmml">p</mi><mi id="S2.p3.6.m6.1.2.2.3" xref="S2.p3.6.m6.1.2.2.3.cmml">thresh</mi></msub><mo id="S2.p3.6.m6.1.2.1" xref="S2.p3.6.m6.1.2.1.cmml">⁢</mo><mrow id="S2.p3.6.m6.1.2.3.2" xref="S2.p3.6.m6.1.2.cmml"><mo stretchy="false" id="S2.p3.6.m6.1.2.3.2.1" xref="S2.p3.6.m6.1.2.cmml">(</mo><mi id="S2.p3.6.m6.1.1" xref="S2.p3.6.m6.1.1.cmml">x</mi><mo stretchy="false" id="S2.p3.6.m6.1.2.3.2.2" xref="S2.p3.6.m6.1.2.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S2.E3.m1.3.3.1" xref="S2.E3.m1.3.3.1.1.cmml"><mrow id="S2.E3.m1.3.3.1.1" xref="S2.E3.m1.3.3.1.1.cmml"><mrow id="S2.E3.m1.3.3.1.1.2" xref="S2.E3.m1.3.3.1.1.2.cmml"><msub id="S2.E3.m1.3.3.1.1.2.2" xref="S2.E3.m1.3.3.1.1.2.2.cmml"><mi id="S2.E3.m1.3.3.1.1.2.2.2" xref="S2.E3.m1.3.3.1.1.2.2.2.cmml">P</mi><mi id="S2.E3.m1.3.3.1.1.2.2.3" xref="S2.E3.m1.3.3.1.1.2.2.3.cmml">move</mi></msub><mo id="S2.E3.m1.3.3.1.1.2.1" xref="S2.E3.m1.3.3.1.1.2.1.cmml">⁢</mo><mrow id="S2.E3.m1.3.3.1.1.2.3.2" xref="S2.E3.m1.3.3.1.1.2.cmml"><mo stretchy="false" id="S2.E3.m1.3.3.1.1.2.3.2.1" xref="S2.E3.m1.3.3.1.1.2.cmml">(</mo><mi id="S2.E3.m1.1.1" xref="S2.E3.m1.1.1.cmml">x</mi><mo stretchy="false" id="S2.E3.m1.3.3.1.1.2.3.2.2" xref="S2.E3.m1.3.3.1.1.2.cmml">)</mo></mrow></mrow><mo id="S2.E3.m1.3.3.1.1.3" xref="S2.E3.m1.3.3.1.1.3.cmml">=</mo><mrow id="S2.E3.m1.3.3.1.1.4" xref="S2.E3.m1.3.3.1.1.4.cmml"><msubsup id="S2.E3.m1.3.3.1.1.4.1" xref="S2.E3.m1.3.3.1.1.4.1.cmml"><mo largeop="true" symmetric="true" id="S2.E3.m1.3.3.1.1.4.1.2.2" xref="S2.E3.m1.3.3.1.1.4.1.2.2.cmml">∫</mo><mi id="S2.E3.m1.3.3.1.1.4.1.2.3" xref="S2.E3.m1.3.3.1.1.4.1.2.3.cmml">x</mi><mi mathvariant="normal" id="S2.E3.m1.3.3.1.1.4.1.3" xref="S2.E3.m1.3.3.1.1.4.1.3.cmml">∞</mi></msubsup><mrow id="S2.E3.m1.3.3.1.1.4.2" xref="S2.E3.m1.3.3.1.1.4.2.cmml"><msub id="S2.E3.m1.3.3.1.1.4.2.2" xref="S2.E3.m1.3.3.1.1.4.2.2.cmml"><mi id="S2.E3.m1.3.3.1.1.4.2.2.2" xref="S2.E3.m1.3.3.1.1.4.2.2.2.cmml">p</mi><mi id="S2.E3.m1.3.3.1.1.4.2.2.3" xref="S2.E3.m1.3.3.1.1.4.2.2.3.cmml">stress</mi></msub><mo id="S2.E3.m1.3.3.1.1.4.2.1" xref="S2.E3.m1.3.3.1.1.4.2.1.cmml">⁢</mo><mrow id="S2.E3.m1.3.3.1.1.4.2.3.2" xref="S2.E3.m1.3.3.1.1.4.2.cmml"><mo stretchy="false" id="S2.E3.m1.3.3.1.1.4.2.3.2.1" xref="S2.E3.m1.3.3.1.1.4.2.cmml">(</mo><mi id="S2.E3.m1.2.2" xref="S2.E3.m1.2.2.cmml">η</mi><mo rspace="4.7pt" stretchy="false" id="S2.E3.m1.3.3.1.1.4.2.3.2.2" xref="S2.E3.m1.3.3.1.1.4.2.cmml">)</mo></mrow><mo id="S2.E3.m1.3.3.1.1.4.2.1a" xref="S2.E3.m1.3.3.1.1.4.2.1.cmml">⁢</mo><mrow id="S2.E3.m1.3.3.1.1.4.2.4" xref="S2.E3.m1.3.3.1.1.4.2.4.cmml"><mo rspace="0pt" id="S2.E3.m1.3.3.1.1.4.2.4.1" xref="S2.E3.m1.3.3.1.1.4.2.4.1.cmml">d</mo><mi id="S2.E3.m1.3.3.1.1.4.2.4.2" xref="S2.E3.m1.3.3.1.1.4.2.4.2.cmml">η</mi></mrow></mrow></mrow><mo id="S2.E3.m1.3.3.1.1.5" xref="S2.E3.m1.3.3.1.1.5.cmml">=</mo><msup id="S2.E3.m1.3.3.1.1.6" xref="S2.E3.m1.3.3.1.1.6.cmml"><mi mathvariant="normal" id="S2.E3.m1.3.3.1.1.6.2" xref="S2.E3.m1.3.3.1.1.6.2.cmml">e</mi><mrow id="S2.E3.m1.3.3.1.1.6.3" xref="S2.E3.m1.3.3.1.1.6.3.cmml"><mo id="S2.E3.m1.3.3.1.1.6.3.1" xref="S2.E3.m1.3.3.1.1.6.3.1.cmml">-</mo><mrow id="S2.E3.m1.3.3.1.1.6.3.2" xref="S2.E3.m1.3.3.1.1.6.3.2.cmml"><mi id="S2.E3.m1.3.3.1.1.6.3.2.2" xref="S2.E3.m1.3.3.1.1.6.3.2.2.cmml">x</mi><mo id="S2.E3.m1.3.3.1.1.6.3.2.1" xref="S2.E3.m1.3.3.1.1.6.3.2.1.cmml">/</mo><mi id="S2.E3.m1.3.3.1.1.6.3.2.3" xref="S2.E3.m1.3.3.1.1.6.3.2.3.cmml">σ</mi></mrow></mrow></msup></mrow><mo id="S2.E3.m1.3.3.1.2" xref="S2.E3.m1.3.3.1.1.cmml">.</mo></mrow></math>

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0201397

Formulas:

1-

- t \sum_{⟨ 𝐢, 𝐣 ⟩, σ} 𝒫 (c_{𝐢 σ}^{†} c_{𝐣, σ} + c_{𝐣, σ}^{†} c_{𝐢, σ}) 𝒫

2-

+ J \sum_{⟨ 𝐢, 𝐣 ⟩} (𝐒_{𝐢} 𝐒_{𝐣} - \frac{1}{4} n_{𝐢} n_{𝐣})

3-

σ = (↑, ↓)

4-

𝐢 = (x, y)

5-

n_{𝐢, σ} = c_{𝐢, σ}^{†} c_{𝐢, σ}

6-

n_{𝐢} = n_{𝐢, ↑} + n_{𝐢, ↓}

7-

𝒫 \equiv \prod_{𝐢} (1 - n_{𝐢, ↑} n_{𝐢, ↓})

8-

g_{y, y^{'}} (x, x^{'}) = \frac{⟨ n_{x, y}^{h} n_{x^{'}, y^{'}}^{h} ⟩}{⟨ n_{x, y}^{h} ⟩ ⟨ n_{x^{'}, y^{'}}^{h} ⟩} n^{h} .

9-

n_{x, y}^{h} = 1 - n_{x, y}

10-

r = (0, 1, \dots)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0209437

Formulas:

1-

J H K L

2-

z_{f i t}

3-

J H K L

4-

J H K L

5-

J H K L

6-

J H K L

7-

J H K L

8-

f_{t p t} (i) = \int S E D (λ (1 + z)) \cdot F T C (i, λ) 𝑑 λ

9-

J, H, K, L

10-

χ^{2} = \sum_{i} {[\frac{f_{o b s} (i) - s \cdot f_{t p t} (i)}{σ (i)}]}^{2},

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1706.05569

Formulas:

1-

vec (𝒙, 𝒚)

2-

𝒙_{t} \in SE (3)

3-

𝑹_{t} \in SO (3)

4-

{\dot{𝒑}}_{t} \in ℝ^{3}

5-

ℒ ≜ {𝒍^{[j]} \in ℝ^{3} | j = 1 : n_{l}}

6-

𝒵_{t} \subset ℝ_{\geq 0}

7-

p (z_{t} | 𝒙_{t}, 𝒍)

8-

p (𝐱_{t} | 𝐱_{t - 1}, 𝐮_{t - 1})

9-

z_{1 : t} ≜ {z_{1}, \dots, z_{t}}

10-

p (𝐱_{0})

Formulas (html):

Correct Categorie: cs

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1212.0928

Formulas:

1-

[u - b] = (u - b) - 1.5 (b - y) = c_{1} + 2 m_{1} + 0.5 (b - y)

2-

u b v y

3-

Q = (U - B) - 0.72 (B - V)

4-

[c 1] = c 1 - 0.2 (b - y)

5-

T_{eff} / \log g

6-

T_{eff} / \log g

7-

V : T_{Q} = (22.59 + 48.57 Q + 70.26 Q^{2}) 10^{3} K

8-

III, IV : T_{Q} = (33.42 + 78.40 Q + 87.19 Q^{2}) 10^{3} K

9-

\log g_{Q} = \frac{T_{Q} (V, IV or III)}{(6.67 + 13.30 Q + 16.67 Q^{2}) 10^{3} K}

10-

T_{eff} / \log g

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1901.04738

Formulas:

1-

conv (S) \cap ℤ^{d} = S

2-

Ω (n \log n)

3-

O (n + h \log r)

4-

conv (S) \cap ℤ^{d} = S

5-

O (n \log n)

6-

O (n \log h)

7-

Θ (n^{⌊ (d - 1) / 2 ⌋})

8-

Ω (n^{⌊ (d - 1) / 2 ⌋})

9-

O (n^{O (d)})

10-

O (n + h \log r)

Formulas (html):

Correct Categorie: cs

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1509.02307

Formulas:

1-

ϵ > 0, M > 0

2-

2 \sqrt{3} \sqrt{area (D)} + δ

3-

area (D) / 4 - δ

4-

c \sqrt{g + 1} \sqrt{area (M)}

5-

F \cap \partial B = \partial F

6-

Γ = (V, E)

7-

E (S, T) = {(u, v) : u \in S, v \in T, (u, v) \in E} .

8-

\partial S = E (S, S^{c})

9-

Γ = (V, E)

10-

| S | \leq | V | / 2

Formulas (html):

Correct Categorie: math

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/hep-th/0402078

Formulas:

1-

Σ \equiv M 2 \cap M 5

2-

d = 0, 1, 2

3-

\frac{1}{2} H H + h J_{5} + J_{8},

4-

h = d b + {B |}_{M 5}

5-

T_{M 2} = T_{M 5} = 2 π

6-

d K = J_{5}, H = d B + K .

7-

K^{'} = K + d Q, B^{'} = B - Q, {Q |}_{M 5} = 0 .

8-

d K = J_{5}

9-

K = \frac{1}{4 {(4 π)}^{2}} ε^{a_{1} \dots a_{5}} {\hat{y}}^{a_{1}} ℱ^{a_{2} a_{3}} ℱ^{a_{4} a_{5}}, ℱ^{a b} = F^{a b} + D {\hat{y}}^{a} D {\hat{y}}^{b},

10-

(a = 1, \dots, 5)

Formulas (html):

Correct Categorie: hep-th

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/nucl-ex/0105003

Formulas:

1-

\sqrt{s_{_{N N}}} = 130

2-

\sqrt{s_{_{N N}}} = 130

3-

\sqrt{s_{_{N N}}} = 130

4-

λ_{2} = ⟨ \cos (2 Δ ϕ) ⟩

5-

Δ ϕ = ϕ_{1} - ϕ_{2}

6-

\frac{d N}{d (Δ ϕ)} \propto [1 + 2 λ_{1} \cos (Δ ϕ) + 2 λ_{2} \cos (2 Δ ϕ)] .

7-

C (Δ ϕ) = \frac{N_{c o r} (Δ ϕ)}{N_{u n c o r} (Δ ϕ)},

8-

N_{c o r} (Δ ϕ)

9-

N_{u n c o r} (Δ ϕ)

10-

C (Δ ϕ)

Formulas (html):

Correct Categorie: nucl-ex

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1812.00810

Formulas:

1-

\min_{G} \max_{D} {𝔼 \log D (x) + 𝔼 \log (1 - D (G (z)))}

2-

\min_{G} \max_{D} J S D (P_{r} ∥ P_{g})

3-

G (z) \sim P_{g}

4-

J S D (\cdot)

5-

- \log D (G (z))

6-

W (P_{r}, P_{g}) = inf_{γ \in (P_{r}, P_{g})} 𝔼_{(x, \tilde{x}) \sim γ} ∥ x - \tilde{x} ∥

7-

\tilde{x} = G (z)

8-

\min_{G} \max_{D \in 𝒟} 𝔼 D (x) - 𝔼 D (G (z))

9-

[- c, c]

10-

L = 𝔼 D (x) - 𝔼 D (\tilde{x}) + λ 𝔼 [{({∥ \nabla_{\hat{x}} D (\hat{x}) ∥}_{2} - 1)}^{2}]

Formulas (html):

Correct Categorie: cs

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/hep-ph/9909308

Formulas:

1-

ℏ = c = k_{B} = 1

2-

ρ_{ν} + ρ_{\bar{ν}} = \int_{0}^{\infty} \frac{d p}{2 π^{2}} p^{2} \sqrt{p^{2} + m_{ν}^{2}} (f_{ν} (p) + f_{\bar{ν}} (p))

3-

f_{ν, \bar{ν}} (p) = \frac{1}{\exp (\frac{p}{T_{ν}} \mp \frac{μ}{T_{ν}}) + 1}

4-

ξ \equiv μ / T_{ν}

5-

p / (y_{ν} T_{0})

6-

T_{d e c} (ξ) \approx 0.2 ξ^{2 / 3} \exp (ξ / 3)

7-

y_{ν} = {(4 / 11)}^{1 / 3}

8-

ρ_{ν} = 10^{4} h^{2} Ω_{ν}

9-

ρ_{c} = 3 H^{2} M_{P}^{2} / 8 π

10-

M_{P} = 1.22 \times 10^{19}

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1007.0218

Formulas:

1-

𝒵 = \sum_{walks} K^{N} ω_{s}^{N_{S}} τ^{N_{I}},

2-

ω_{s} = \exp (β ε_{S})

3-

τ = \exp (β ε)

4-

⟨ N ⟩ = K \frac{\partial \ln 𝒵}{\partial K} .

5-

K = K^{*} (ω_{s}, τ)

6-

⟨ N ⟩ \sim {(K^{*} (ω_{s}, τ) - K)}^{- 1},

7-

ω_{s} = ω_{s}^{*}

8-

ω_{s} \leq ω_{s}^{*}

9-

ω_{s} > ω_{s}^{*}

10-

ω_{s} = ω_{s}^{*}

Formulas (html):

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id="S2.E1.m1.1.1.1.1.3.2.3" xref="S2.E1.m1.1.1.1.1.3.2.3.cmml"><mi id="S2.E1.m1.1.1.1.1.3.2.3.2.2" xref="S2.E1.m1.1.1.1.1.3.2.3.2.2.cmml">ω</mi><mi id="S2.E1.m1.1.1.1.1.3.2.3.2.3" xref="S2.E1.m1.1.1.1.1.3.2.3.2.3.cmml">s</mi><msub id="S2.E1.m1.1.1.1.1.3.2.3.3" xref="S2.E1.m1.1.1.1.1.3.2.3.3.cmml"><mi id="S2.E1.m1.1.1.1.1.3.2.3.3.2" xref="S2.E1.m1.1.1.1.1.3.2.3.3.2.cmml">N</mi><mi id="S2.E1.m1.1.1.1.1.3.2.3.3.3" xref="S2.E1.m1.1.1.1.1.3.2.3.3.3.cmml">S</mi></msub></msubsup><mo id="S2.E1.m1.1.1.1.1.3.2.1a" xref="S2.E1.m1.1.1.1.1.3.2.1.cmml">⁢</mo><msup id="S2.E1.m1.1.1.1.1.3.2.4" xref="S2.E1.m1.1.1.1.1.3.2.4.cmml"><mi id="S2.E1.m1.1.1.1.1.3.2.4.2" xref="S2.E1.m1.1.1.1.1.3.2.4.2.cmml">τ</mi><msub id="S2.E1.m1.1.1.1.1.3.2.4.3" xref="S2.E1.m1.1.1.1.1.3.2.4.3.cmml"><mi id="S2.E1.m1.1.1.1.1.3.2.4.3.2" xref="S2.E1.m1.1.1.1.1.3.2.4.3.2.cmml">N</mi><mi id="S2.E1.m1.1.1.1.1.3.2.4.3.3" xref="S2.E1.m1.1.1.1.1.3.2.4.3.3.cmml">I</mi></msub></msup></mrow></mrow></mrow><mo id="S2.E1.m1.1.1.1.2" xref="S2.E1.m1.1.1.1.1.cmml">,</mo></mrow></math>, <math><mrow id="S2.p3.2.m2.2.2" xref="S2.p3.2.m2.2.2.cmml"><msub id="S2.p3.2.m2.2.2.3" xref="S2.p3.2.m2.2.2.3.cmml"><mi id="S2.p3.2.m2.2.2.3.2" xref="S2.p3.2.m2.2.2.3.2.cmml">ω</mi><mi id="S2.p3.2.m2.2.2.3.3" xref="S2.p3.2.m2.2.2.3.3.cmml">s</mi></msub><mo id="S2.p3.2.m2.2.2.2" xref="S2.p3.2.m2.2.2.2.cmml">=</mo><mrow id="S2.p3.2.m2.2.2.1.1" xref="S2.p3.2.m2.2.2.1.2.cmml"><mi id="S2.p3.2.m2.1.1" xref="S2.p3.2.m2.1.1.cmml">exp</mi><mo id="S2.p3.2.m2.2.2.1.1a" xref="S2.p3.2.m2.2.2.1.2.cmml">⁡</mo><mrow id="S2.p3.2.m2.2.2.1.1.1" xref="S2.p3.2.m2.2.2.1.2.cmml"><mo stretchy="false" id="S2.p3.2.m2.2.2.1.1.1.2" xref="S2.p3.2.m2.2.2.1.2.cmml">(</mo><mrow id="S2.p3.2.m2.2.2.1.1.1.1" xref="S2.p3.2.m2.2.2.1.1.1.1.cmml"><mi id="S2.p3.2.m2.2.2.1.1.1.1.2" xref="S2.p3.2.m2.2.2.1.1.1.1.2.cmml">β</mi><mo id="S2.p3.2.m2.2.2.1.1.1.1.1" xref="S2.p3.2.m2.2.2.1.1.1.1.1.cmml">⁢</mo><msub id="S2.p3.2.m2.2.2.1.1.1.1.3" xref="S2.p3.2.m2.2.2.1.1.1.1.3.cmml"><mi id="S2.p3.2.m2.2.2.1.1.1.1.3.2" xref="S2.p3.2.m2.2.2.1.1.1.1.3.2.cmml">ε</mi><mi id="S2.p3.2.m2.2.2.1.1.1.1.3.3" xref="S2.p3.2.m2.2.2.1.1.1.1.3.3.cmml">S</mi></msub></mrow><mo stretchy="false" id="S2.p3.2.m2.2.2.1.1.1.3" xref="S2.p3.2.m2.2.2.1.2.cmml">)</mo></mrow></mrow></mrow></math>, <math><mrow id="S2.p3.3.m3.2.2" xref="S2.p3.3.m3.2.2.cmml"><mi id="S2.p3.3.m3.2.2.3" xref="S2.p3.3.m3.2.2.3.cmml">τ</mi><mo id="S2.p3.3.m3.2.2.2" xref="S2.p3.3.m3.2.2.2.cmml">=</mo><mrow id="S2.p3.3.m3.2.2.1.1" xref="S2.p3.3.m3.2.2.1.2.cmml"><mi id="S2.p3.3.m3.1.1" xref="S2.p3.3.m3.1.1.cmml">exp</mi><mo id="S2.p3.3.m3.2.2.1.1a" xref="S2.p3.3.m3.2.2.1.2.cmml">⁡</mo><mrow id="S2.p3.3.m3.2.2.1.1.1" xref="S2.p3.3.m3.2.2.1.2.cmml"><mo stretchy="false" id="S2.p3.3.m3.2.2.1.1.1.2" xref="S2.p3.3.m3.2.2.1.2.cmml">(</mo><mrow id="S2.p3.3.m3.2.2.1.1.1.1" xref="S2.p3.3.m3.2.2.1.1.1.1.cmml"><mi id="S2.p3.3.m3.2.2.1.1.1.1.2" xref="S2.p3.3.m3.2.2.1.1.1.1.2.cmml">β</mi><mo id="S2.p3.3.m3.2.2.1.1.1.1.1" xref="S2.p3.3.m3.2.2.1.1.1.1.1.cmml">⁢</mo><mi id="S2.p3.3.m3.2.2.1.1.1.1.3" xref="S2.p3.3.m3.2.2.1.1.1.1.3.cmml">ε</mi></mrow><mo stretchy="false" id="S2.p3.3.m3.2.2.1.1.1.3" xref="S2.p3.3.m3.2.2.1.2.cmml">)</mo></mrow></mrow></mrow></math>, <math><mrow id="S2.E2.m1.2.2.1" xref="S2.E2.m1.2.2.1.1.cmml"><mrow id="S2.E2.m1.2.2.1.1" xref="S2.E2.m1.2.2.1.1.cmml"><mrow id="S2.E2.m1.2.2.1.1.2.2" xref="S2.E2.m1.2.2.1.1.2.1.cmml"><mo stretchy="false" id="S2.E2.m1.2.2.1.1.2.2.1" xref="S2.E2.m1.2.2.1.1.2.1.1.cmml">⟨</mo><mi id="S2.E2.m1.1.1" xref="S2.E2.m1.1.1.cmml">N</mi><mo stretchy="false" id="S2.E2.m1.2.2.1.1.2.2.2" xref="S2.E2.m1.2.2.1.1.2.1.1.cmml">⟩</mo></mrow><mo id="S2.E2.m1.2.2.1.1.1" xref="S2.E2.m1.2.2.1.1.1.cmml">=</mo><mrow id="S2.E2.m1.2.2.1.1.3" xref="S2.E2.m1.2.2.1.1.3.cmml"><mi id="S2.E2.m1.2.2.1.1.3.2" xref="S2.E2.m1.2.2.1.1.3.2.cmml">K</mi><mo id="S2.E2.m1.2.2.1.1.3.1" xref="S2.E2.m1.2.2.1.1.3.1.cmml">⁢</mo><mfrac id="S2.E2.m1.2.2.1.1.3.3" xref="S2.E2.m1.2.2.1.1.3.3.cmml"><mrow id="S2.E2.m1.2.2.1.1.3.3.2" xref="S2.E2.m1.2.2.1.1.3.3.2.cmml"><mrow id="S2.E2.m1.2.2.1.1.3.3.2.1" xref="S2.E2.m1.2.2.1.1.3.3.2.1.cmml"><mo id="S2.E2.m1.2.2.1.1.3.3.2.1.1" xref="S2.E2.m1.2.2.1.1.3.3.2.1.1.cmml">∂</mo><mo id="S2.E2.m1.2.2.1.1.3.3.2.1a" xref="S2.E2.m1.2.2.1.1.3.3.2.1.cmml">⁡</mo><mi id="S2.E2.m1.2.2.1.1.3.3.2.1.2" xref="S2.E2.m1.2.2.1.1.3.3.2.1.2.cmml">ln</mi></mrow><mo id="S2.E2.m1.2.2.1.1.3.3.2a" xref="S2.E2.m1.2.2.1.1.3.3.2.cmml">⁡</mo><mi class="ltx_font_mathcaligraphic" id="S2.E2.m1.2.2.1.1.3.3.2.2" xref="S2.E2.m1.2.2.1.1.3.3.2.2.cmml">𝒵</mi></mrow><mrow id="S2.E2.m1.2.2.1.1.3.3.3" xref="S2.E2.m1.2.2.1.1.3.3.3.cmml"><mo id="S2.E2.m1.2.2.1.1.3.3.3.1" xref="S2.E2.m1.2.2.1.1.3.3.3.1.cmml">∂</mo><mo id="S2.E2.m1.2.2.1.1.3.3.3a" xref="S2.E2.m1.2.2.1.1.3.3.3.cmml">⁡</mo><mi id="S2.E2.m1.2.2.1.1.3.3.3.2" xref="S2.E2.m1.2.2.1.1.3.3.3.2.cmml">K</mi></mrow></mfrac></mrow></mrow><mo id="S2.E2.m1.2.2.1.2" xref="S2.E2.m1.2.2.1.1.cmml">.</mo></mrow></math>, <math><mrow id="S2.p4.4.m3.2.2" xref="S2.p4.4.m3.2.2.cmml"><mi id="S2.p4.4.m3.2.2.3" xref="S2.p4.4.m3.2.2.3.cmml">K</mi><mo id="S2.p4.4.m3.2.2.2" xref="S2.p4.4.m3.2.2.2.cmml">=</mo><mrow id="S2.p4.4.m3.2.2.1" xref="S2.p4.4.m3.2.2.1.cmml"><msup id="S2.p4.4.m3.2.2.1.3" xref="S2.p4.4.m3.2.2.1.3.cmml"><mi id="S2.p4.4.m3.2.2.1.3.2" xref="S2.p4.4.m3.2.2.1.3.2.cmml">K</mi><mo id="S2.p4.4.m3.2.2.1.3.3" xref="S2.p4.4.m3.2.2.1.3.3.cmml">*</mo></msup><mo id="S2.p4.4.m3.2.2.1.2" xref="S2.p4.4.m3.2.2.1.2.cmml">⁢</mo><mrow id="S2.p4.4.m3.2.2.1.1.1" xref="S2.p4.4.m3.2.2.1.1.2.cmml"><mo stretchy="false" id="S2.p4.4.m3.2.2.1.1.1.2" xref="S2.p4.4.m3.2.2.1.1.2.cmml">(</mo><msub id="S2.p4.4.m3.2.2.1.1.1.1" xref="S2.p4.4.m3.2.2.1.1.1.1.cmml"><mi id="S2.p4.4.m3.2.2.1.1.1.1.2" xref="S2.p4.4.m3.2.2.1.1.1.1.2.cmml">ω</mi><mi id="S2.p4.4.m3.2.2.1.1.1.1.3" xref="S2.p4.4.m3.2.2.1.1.1.1.3.cmml">s</mi></msub><mo id="S2.p4.4.m3.2.2.1.1.1.3" xref="S2.p4.4.m3.2.2.1.1.2.cmml">,</mo><mi id="S2.p4.4.m3.1.1" xref="S2.p4.4.m3.1.1.cmml">τ</mi><mo stretchy="false" id="S2.p4.4.m3.2.2.1.1.1.4" xref="S2.p4.4.m3.2.2.1.1.2.cmml">)</mo></mrow></mrow></mrow></math>, <math><mrow id="S2.E3.m1.3.3.1" xref="S2.E3.m1.3.3.1.1.cmml"><mrow id="S2.E3.m1.3.3.1.1" xref="S2.E3.m1.3.3.1.1.cmml"><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.m1.3.3.1.1.3.1.1.cmml">⟨</mo><mi id="S2.E3.m1.1.1" xref="S2.E3.m1.1.1.cmml">N</mi><mo stretchy="false" id="S2.E3.m1.3.3.1.1.3.2.2" xref="S2.E3.m1.3.3.1.1.3.1.1.cmml">⟩</mo></mrow><mo id="S2.E3.m1.3.3.1.1.2" xref="S2.E3.m1.3.3.1.1.2.cmml">∼</mo><msup id="S2.E3.m1.3.3.1.1.1" xref="S2.E3.m1.3.3.1.1.1.cmml"><mrow id="S2.E3.m1.3.3.1.1.1.1.1" xref="S2.E3.m1.3.3.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S2.E3.m1.3.3.1.1.1.1.1.2" xref="S2.E3.m1.3.3.1.1.1.1.1.1.cmml">(</mo><mrow id="S2.E3.m1.3.3.1.1.1.1.1.1" xref="S2.E3.m1.3.3.1.1.1.1.1.1.cmml"><mrow id="S2.E3.m1.3.3.1.1.1.1.1.1.1" xref="S2.E3.m1.3.3.1.1.1.1.1.1.1.cmml"><msup id="S2.E3.m1.3.3.1.1.1.1.1.1.1.3" xref="S2.E3.m1.3.3.1.1.1.1.1.1.1.3.cmml"><mi id="S2.E3.m1.3.3.1.1.1.1.1.1.1.3.2" xref="S2.E3.m1.3.3.1.1.1.1.1.1.1.3.2.cmml">K</mi><mo id="S2.E3.m1.3.3.1.1.1.1.1.1.1.3.3" xref="S2.E3.m1.3.3.1.1.1.1.1.1.1.3.3.cmml">*</mo></msup><mo id="S2.E3.m1.3.3.1.1.1.1.1.1.1.2" xref="S2.E3.m1.3.3.1.1.1.1.1.1.1.2.cmml">⁢</mo><mrow id="S2.E3.m1.3.3.1.1.1.1.1.1.1.1.1" xref="S2.E3.m1.3.3.1.1.1.1.1.1.1.1.2.cmml"><mo stretchy="false" id="S2.E3.m1.3.3.1.1.1.1.1.1.1.1.1.2" xref="S2.E3.m1.3.3.1.1.1.1.1.1.1.1.2.cmml">(</mo><msub id="S2.E3.m1.3.3.1.1.1.1.1.1.1.1.1.1" xref="S2.E3.m1.3.3.1.1.1.1.1.1.1.1.1.1.cmml"><mi id="S2.E3.m1.3.3.1.1.1.1.1.1.1.1.1.1.2" xref="S2.E3.m1.3.3.1.1.1.1.1.1.1.1.1.1.2.cmml">ω</mi><mi id="S2.E3.m1.3.3.1.1.1.1.1.1.1.1.1.1.3" xref="S2.E3.m1.3.3.1.1.1.1.1.1.1.1.1.1.3.cmml">s</mi></msub><mo id="S2.E3.m1.3.3.1.1.1.1.1.1.1.1.1.3" xref="S2.E3.m1.3.3.1.1.1.1.1.1.1.1.2.cmml">,</mo><mi id="S2.E3.m1.2.2" xref="S2.E3.m1.2.2.cmml">τ</mi><mo stretchy="false" id="S2.E3.m1.3.3.1.1.1.1.1.1.1.1.1.4" xref="S2.E3.m1.3.3.1.1.1.1.1.1.1.1.2.cmml">)</mo></mrow></mrow><mo id="S2.E3.m1.3.3.1.1.1.1.1.1.2" xref="S2.E3.m1.3.3.1.1.1.1.1.1.2.cmml">-</mo><mi id="S2.E3.m1.3.3.1.1.1.1.1.1.3" xref="S2.E3.m1.3.3.1.1.1.1.1.1.3.cmml">K</mi></mrow><mo stretchy="false" id="S2.E3.m1.3.3.1.1.1.1.1.3" xref="S2.E3.m1.3.3.1.1.1.1.1.1.cmml">)</mo></mrow><mrow id="S2.E3.m1.3.3.1.1.1.3" xref="S2.E3.m1.3.3.1.1.1.3.cmml"><mo id="S2.E3.m1.3.3.1.1.1.3.1" xref="S2.E3.m1.3.3.1.1.1.3.1.cmml">-</mo><mn id="S2.E3.m1.3.3.1.1.1.3.2" xref="S2.E3.m1.3.3.1.1.1.3.2.cmml">1</mn></mrow></msup></mrow><mo id="S2.E3.m1.3.3.1.2" xref="S2.E3.m1.3.3.1.1.cmml">,</mo></mrow></math>, <math><mrow id="S2.p5.4.m4.1.1" xref="S2.p5.4.m4.1.1.cmml"><msub id="S2.p5.4.m4.1.1.2" xref="S2.p5.4.m4.1.1.2.cmml"><mi id="S2.p5.4.m4.1.1.2.2" xref="S2.p5.4.m4.1.1.2.2.cmml">ω</mi><mi id="S2.p5.4.m4.1.1.2.3" xref="S2.p5.4.m4.1.1.2.3.cmml">s</mi></msub><mo id="S2.p5.4.m4.1.1.1" xref="S2.p5.4.m4.1.1.1.cmml">=</mo><msubsup id="S2.p5.4.m4.1.1.3" xref="S2.p5.4.m4.1.1.3.cmml"><mi id="S2.p5.4.m4.1.1.3.2.2" xref="S2.p5.4.m4.1.1.3.2.2.cmml">ω</mi><mi id="S2.p5.4.m4.1.1.3.2.3" xref="S2.p5.4.m4.1.1.3.2.3.cmml">s</mi><mo id="S2.p5.4.m4.1.1.3.3" xref="S2.p5.4.m4.1.1.3.3.cmml">*</mo></msubsup></mrow></math>, <math><mrow id="S2.p5.5.m5.1.1" xref="S2.p5.5.m5.1.1.cmml"><msub id="S2.p5.5.m5.1.1.2" xref="S2.p5.5.m5.1.1.2.cmml"><mi id="S2.p5.5.m5.1.1.2.2" xref="S2.p5.5.m5.1.1.2.2.cmml">ω</mi><mi id="S2.p5.5.m5.1.1.2.3" xref="S2.p5.5.m5.1.1.2.3.cmml">s</mi></msub><mo id="S2.p5.5.m5.1.1.1" xref="S2.p5.5.m5.1.1.1.cmml">≤</mo><msubsup id="S2.p5.5.m5.1.1.3" xref="S2.p5.5.m5.1.1.3.cmml"><mi id="S2.p5.5.m5.1.1.3.2.2" xref="S2.p5.5.m5.1.1.3.2.2.cmml">ω</mi><mi id="S2.p5.5.m5.1.1.3.2.3" xref="S2.p5.5.m5.1.1.3.2.3.cmml">s</mi><mo id="S2.p5.5.m5.1.1.3.3" xref="S2.p5.5.m5.1.1.3.3.cmml">*</mo></msubsup></mrow></math>, <math><mrow id="S2.p5.10.m10.1.1" xref="S2.p5.10.m10.1.1.cmml"><msub id="S2.p5.10.m10.1.1.2" xref="S2.p5.10.m10.1.1.2.cmml"><mi id="S2.p5.10.m10.1.1.2.2" xref="S2.p5.10.m10.1.1.2.2.cmml">ω</mi><mi id="S2.p5.10.m10.1.1.2.3" xref="S2.p5.10.m10.1.1.2.3.cmml">s</mi></msub><mo id="S2.p5.10.m10.1.1.1" xref="S2.p5.10.m10.1.1.1.cmml">></mo><msubsup id="S2.p5.10.m10.1.1.3" xref="S2.p5.10.m10.1.1.3.cmml"><mi id="S2.p5.10.m10.1.1.3.2.2" xref="S2.p5.10.m10.1.1.3.2.2.cmml">ω</mi><mi id="S2.p5.10.m10.1.1.3.2.3" xref="S2.p5.10.m10.1.1.3.2.3.cmml">s</mi><mo id="S2.p5.10.m10.1.1.3.3" xref="S2.p5.10.m10.1.1.3.3.cmml">*</mo></msubsup></mrow></math>, <math><mrow id="S2.p5.14.m14.1.1" xref="S2.p5.14.m14.1.1.cmml"><msub id="S2.p5.14.m14.1.1.2" xref="S2.p5.14.m14.1.1.2.cmml"><mi id="S2.p5.14.m14.1.1.2.2" xref="S2.p5.14.m14.1.1.2.2.cmml">ω</mi><mi id="S2.p5.14.m14.1.1.2.3" xref="S2.p5.14.m14.1.1.2.3.cmml">s</mi></msub><mo id="S2.p5.14.m14.1.1.1" xref="S2.p5.14.m14.1.1.1.cmml">=</mo><msubsup id="S2.p5.14.m14.1.1.3" xref="S2.p5.14.m14.1.1.3.cmml"><mi id="S2.p5.14.m14.1.1.3.2.2" xref="S2.p5.14.m14.1.1.3.2.2.cmml">ω</mi><mi id="S2.p5.14.m14.1.1.3.2.3" xref="S2.p5.14.m14.1.1.3.2.3.cmml">s</mi><mo id="S2.p5.14.m14.1.1.3.3" xref="S2.p5.14.m14.1.1.3.3.cmml">*</mo></msubsup></mrow></math>

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1204.2947

Formulas:

1-

𝒜_{z z} > 0

2-

D_{g s} = 2.87

3-

D_{e s} = 1.42

4-

I^{(N)} = 1

5-

ℋ_{0} = D_{g s} {\hat{S}}_{z}^{2} + γ_{e} B {\hat{S}}_{z} + γ_{n}^{(N)} B {\hat{I}}_{z}^{(N)} + 𝒬_{N} {({\hat{I}}_{z}^{(N)})}^{2} + \hat{𝐒} \cdot 𝒜_{N} \cdot {\hat{𝐈}}^{(𝐍)}

6-

𝒜_{N}^{hs} = - 2.16

7-

I^{(C)} = 1 / 2

8-

ℋ = ℋ_{0} + γ_{n} B {\hat{I}}_{z}^{(C)} + \hat{𝐒} \cdot 𝒜_{C} \cdot {\hat{𝐈}}^{(C)}

9-

𝒜_{C} = (\begin{matrix} 𝒜_{x x} & 𝒜_{x y} & 𝒜_{x z} \\ 𝒜_{y x} & 𝒜_{y y} & 𝒜_{y z} \\ 𝒜_{z x} & 𝒜_{z y} & 𝒜_{z z} \end{matrix}) .

10-

ℋ = ℋ_{0} + γ_{n} B {\hat{I}}_{z}^{(C)} + {\hat{S}}_{z} \sum_{i} 𝒜_{z i} {\hat{I}}_{i}^{(C)} .

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0206143

Formulas:

1-

| [M] | \leq

2-

\log (N / N_{t o t})

3-

\log (N / N_{H})

4-

ξ_{t} = 2.4 \pm 0.3

5-

\log (N / N_{t o t})

6-

\log (N / N_{t o t})

7-

\log (N / N_{t o t})

8-

\log (N / N_{t o t})

9-

\log (N / N_{t o t})

10-

\log (C l / N_{t o t})

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1012.1259

Formulas:

1-

a^{3} Π_{1}, v = 0

2-

a^{3} Π_{1}, v = 0

3-

X^{1} Σ^{+}, v " = 0

4-

a^{3} Π_{1}, v = 0, J = 1

5-

a^{3} Π_{1}, v = 0

6-

J = 2 \leftarrow J = 1

7-

a^{3} Π_{1}, v = 0

8-

J = 2 \leftarrow J = 1

9-

Δ M = \pm 1

10-

a^{3} Π_{1}, v = 0

Formulas (html):

Correct Categorie: physics

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1306.2398

Formulas:

1-

𝒩 = (2, 2)

2-

U {(1)}_{R}

3-

U {(1)}_{R}

4-

U {(1)}_{R}

5-

𝒩 = (2, 2)

6-

O S p (2 | 2) ≅ S U (2 | 1),

7-

S U (2) \times U {(1)}_{R}

8-

S U (2)

9-

U {(1)}_{R}

10-

λ ψ = λ^{α} ε_{α β} ψ^{β} = ψ λ,

Formulas (html):

Correct Categorie: hep-th

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1110.2304

Formulas:

1-

P = P_{b} {[\frac{T_{b}}{T_{b} + L_{b} \cdot (h - h_{b})}]}^{\frac{g_{0} \cdot M_{0}}{R^{*} \cdot L_{b}}},

2-

P = P_{0} {(1 - 0.0065 \frac{h}{T_{0}})}^{5.256},

3-

G_{1} = \frac{\sqrt{n (n - 1)}}{n - 2} \cdot \frac{m_{3}}{m_{2}^{\frac{3}{2}}},

4-

m_{3} = \frac{1}{n} \sum_{i = 1}^{n} {(x_{i} - \bar{x})}^{3}

5-

m_{2} = \frac{1}{n} \sum_{i = 1}^{n} {(x_{i} - \bar{x})}^{2}

6-

Z = \frac{G_{1}}{S E S},

7-

S E S = \sqrt{\frac{6 n (n - 1)}{(n - 2) (n + 1) (n + 3)}} .

8-

0 \leq W_{s p} < 3

9-

3 \leq W_{s p} < 10

10-

10 \leq W_{s p} \leq 15

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1810.11030

Formulas:

1-

M_{ν} := \sum m_{ν} \in {0, 0.1, 0.15} eV

2-

f_{R 0} = - 10^{- 5}

3-

z_{s} \in {0.5, 1.0, 1.5, 2.0, 3.0, 4.0}

4-

j \in {1, \dots, j_{\max}}

5-

1 \times 4 \times 5 \times 100

6-

8 \times 4 \times 5 \times 100

7-

8 \times 4 \times 5 \times 100

8-

8 \times 4 \times 5 \times 20

9-

8 \times 4 \times 5 \times 20

10-

8 \times 4 \times 5 \times 10

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/9904195

Formulas:

1-

\frac{\partial 𝐮}{\partial t} + \sum_{i = 1}^{3} \frac{\partial 𝐟^{i} (𝐮)}{\partial x_{i}} = 0

2-

ℬ^{i} = \frac{\partial 𝐟^{i} (𝐮)}{\partial 𝐮} .

3-

\frac{d 𝐮_{i, j, k} (t)}{d t} = - \frac{{\hat{𝐟}}_{i + \frac{1}{2}, j, k} - {\hat{𝐟}}_{i - \frac{1}{2}, j, k}}{Δ x} - \frac{{\hat{𝐠}}_{i, j + \frac{1}{2}, k} - {\hat{𝐠}}_{i, j - \frac{1}{2}, k}}{Δ y} - \frac{{\hat{𝐡}}_{i, j, k + \frac{1}{2}} - {\hat{𝐡}}_{i, j, k - \frac{1}{2}}}{Δ z}

4-

{\hat{𝐟}}_{i + \frac{1}{2}, j, k}

5-

{\hat{𝐠}}_{i, j + \frac{1}{2}, k}

6-

{\hat{𝐡}}_{i, j, k + \frac{1}{2}}

7-

𝐮 = 𝐮 (x_{1}, t)

8-

\hat{𝐟} (𝐮^{L}, 𝐮^{R}) = \frac{1}{2} ((ℐ + {\tilde{ℐ}}^{L}) 𝐟^{L} + (ℐ - {\tilde{ℐ}}^{R}) 𝐟^{R} + (𝒬^{L} 𝐮^{L} - 𝒬^{R} 𝐮^{R}))

9-

{\tilde{ℐ}}^{L, R} = \sum_{p = 1}^{d} b_{p} 𝐥_{p}^{L, R} 𝐫_{p}^{L, R}

10-

𝒬^{L, R} = \sum_{p = 1}^{d} c_{p} 𝐥_{p}^{L, R} 𝐫_{p}^{L, R}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/quant-ph/0703030

Formulas:

1-

α + β + γ = - 1

2-

{- \frac{1}{2} [M^{α} (𝒙) \partial_{i} M^{β} (𝒙) \partial_{i} M^{γ} (𝒙) + M^{γ} (𝒙) \partial_{i} M^{β} (𝒙) \partial_{i} M^{α} (𝒙)] + V (𝒙)} ψ (𝒙) = E ψ (𝒙),

3-

𝒙 \equiv (x_{1}, x_{2}, x_{3}) = (x, y, z)

4-

\partial_{i} \equiv \partial / \partial x_{i}

5-

m (𝒙) = m_{0} M (𝒙)

6-

ℏ = 2 m_{0} = 1

7-

V_{eff} (𝒙)

8-

H ψ (𝒙) \equiv (- \partial_{i} \frac{1}{M (𝒙)} \partial_{i} + V_{eff} (𝒙)) ψ (𝒙) = E ψ (𝒙),

9-

V_{eff} (𝒙)

10-

V_{eff} (𝒙) = V (𝒙) + \frac{1}{2} (β + 1) \frac{Δ M}{M^{2}} - [α (α + β + 1) + β + 1] \frac{(\partial_{i} M) (\partial_{i} M)}{M^{3}} .

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0307522

Formulas:

1-

n \sim τ^{- d / 4}

2-

γ \partial_{t} ϕ (t, x) = \partial_{x}^{2} ϕ (t, x) - a (t) ϕ (t, x) - λ ϕ^{3} (t, x) + η (t, x),

3-

η (t, x)

4-

⟨ η (t, x) ⟩ = 0,

5-

⟨ η (t, x) η (t^{'}, x^{'}) ⟩ = \frac{2 π γ}{β} δ (x - x^{'}) δ (t - t^{'}) .

6-

n = \frac{1}{π} \sqrt{\frac{⟨ ϕ^{', 2} ⟩}{⟨ ϕ^{2} ⟩}} .

7-

n \sim \frac{1}{τ^{\frac{1}{4}}} .

8-

𝒟 (t, x)

9-

γ \partial_{t} ϕ (t, x) = \partial_{x}^{2} ϕ (t, x) - a (t) ϕ (t, x) - λ ϕ^{3} (t, x) + η (t, x) + 𝒟 (t, x) .

10-

n (t, x) = lim_{L \to 0} \frac{⟨ N ⟩}{2 L} = lim_{L \to 0} \frac{1}{2 L} ⟨ \sum_{i} \frac{| ϕ^{'} (t, x_{i}) |}{| ϕ^{'} (t, x_{i}) |} ⟩ .

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/2007.12970

Formulas:

1-

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

2-

𝒜 = {a_{1}, a_{2}, \dots, a_{n}} .

3-

{a_{i} + a_{j} | (i, j) \in E (G_{n})} .

4-

𝒜 \cdot_{G_{n}} 𝒜 = {a_{i} \cdot a_{j} | (i, j) \in E (G_{n})} .

5-

| 𝒜 +_{G_{n}} 𝒜 | + | 𝒜 \cdot_{G_{n}} 𝒜 | \geq {| 𝒜 |}^{1 + c - ε} .

6-

| 𝒜 | = m \geq m_{0}

7-

Ω (m^{5 / 3} / \log^{1 / 3} m)

8-

| 𝒜 +_{G_{m}} 𝒜 | + | 𝒜 \cdot_{G_{m}} 𝒜 | = O ({(| 𝒜 | \log | 𝒜 |)}^{4 / 3}) .

9-

m^{2 - 2 c}

10-

c = 1 / 3 .

Formulas (html):

Correct Categorie: math

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0909.0960

Formulas:

1-

λ F_{λ} \propto λ^{n}

2-

- 2 < n < 0

3-

- 3 < n < - 2

4-

3 ≲ A_{V} < 9

5-

0.3 ≲ A_{K} < 1

6-

E W (10 μ m)

7-

n_{13 - 31} = \frac{\log (λ_{31} F_{λ_{31}}) - \log (λ_{13} F_{λ_{13}})}{\log (λ_{31}) - \log (λ_{13})}

8-

λ F_{λ} \propto λ^{n}

9-

E W (10 μ m) = \int_{8 μ m}^{13 μ m} \frac{F_{λ} - F_{λ, c o n t}}{F_{λ, c o n t}} 𝑑 λ

10-

E W (10 μ m)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/gr-qc/0506133

Formulas:

1-

y ≺ z \Rightarrow x ≺ z

2-

| Past (x) \cap Fut (y) | < \infty

3-

x, y, z \in C

4-

Past (y) = {x | x ≺ y}

5-

Fut (y) = {x | y ≺ x}

6-

I^{+} (p_{1}) \cap I^{-} (p_{2})

7-

I^{\pm} (x)

8-

\exp [- ρ vol (I^{+} (p_{1}) \cap I^{-} (p_{2}))]

9-

vol (I^{+} (p_{1}) \cap I^{-} (p_{2})) \overset{<}{\sim} 1 / ρ

10-

x \in Past (A)

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0907.3650

Formulas:

1-

γ = - d \ln ε / d \ln V

2-

γ (T, V) = β V / χ_{S} C_{p}

3-

β = {(\partial l n V / \partial T)}_{P}

4-

χ_{S} = - {(\partial l n V / \partial P)}_{S}

5-

γ = \sum_{r} γ_{r} C_{r} / \sum_{r} C_{r}

6-

\approx 4.4 \cdot 10^{- 3}

7-

\approx 9 \cdot 10^{- 4}

8-

T_{c}^{o n s e t} \approx 14

9-

d T_{c} / d p_{i} = \frac{V_{m} Δ α_{i}}{Δ C_{p} / T_{c}}

10-

i = a b, c

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1610.06979

Formulas:

1-

d_{G} (v)

2-

G [X, Y]

3-

V (G_{1} + G_{2}) = V (G_{1}) \cup V (G_{2})

4-

E (G_{1} + G_{2}) = E (G_{1}) \cup E (G_{2})

5-

V (G_{1} \lor G_{2}) = V (G_{1}) \cup V (G_{2})

6-

E (G_{1} \lor G_{2}) = E (G_{1} \lor G_{2}) \cup {x y : x \in V (G_{1}), y \in V (G_{2})}

7-

K_{n - 1} + e

8-

K_{n - 1} + v

9-

{[V]}^{2} ∖ E (G)

10-

d_{G} (u, v)

Formulas (html):

Correct Categorie: math

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1608.07520

Formulas:

1-

𝔻 := {z \in ℂ : | z | < 1}

2-

f (0) = 0 = f^{'} (0) - 1

3-

\log \frac{f (z)}{z} = 2 \sum_{n = 1}^{\infty} γ_{n} z^{n}

4-

𝔻 := {z \in ℂ : | z | < 1}

5-

f (z) = z + \sum_{n = 2}^{\infty} a_{n} z^{n} .

6-

Re (z f^{'} (z) / f (z)) > 0

7-

Re (1 + (z f^{''} (z) / f^{'} (z))) > 0

8-

z f^{'} \in 𝒮^{*}

9-

α \in (- π / 2, π / 2)

10-

Re (e^{i α} \frac{z f^{'} (z)}{g (z)}) > 0, z \in 𝔻 .

Formulas (html):

Correct Categorie: math

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/9710165

Formulas:

1-

3 ″ < Δ θ < 10 ″

2-

3 ″ < Δ θ < 10 ″

3-

| Δ v | < \sim 10^{3} km s^{- 1}

4-

P_{p a i r} \sim 2 \times 10^{- 3}

5-

4 \overset{''}{.} 8

6-

3 \overset{''}{.} 3

7-

6 \overset{''}{.} 1

8-

3 \overset{''}{.} 1

9-

6 \overset{''}{.} 1

10-

3 \overset{''}{.} 1

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1103.5224

Formulas:

1-

η = 1 - T_{C} / T_{H}

2-

f (θ, p, t)

3-

\frac{\partial f}{\partial t} + p \frac{\partial f}{\partial θ} - \frac{d V}{d θ} \frac{\partial f}{\partial p} = 0,

4-

V (θ) [f]

5-

V (θ) [f]

6-

V (θ) [f] = 1 - M [f] \cos (θ) + h \cos (θ)

7-

M [f] = \int_{- π}^{π} \int_{- \infty}^{\infty} f (θ, p, t) \cos θ d θ d p,

8-

e [f] = \int \int (p^{2} / 2) f (θ, p, t) d θ d p - (M^{2} - 1) / 2 + h M

9-

ρ (θ, p, η)

10-

\bar{f} (θ, p) = \int ρ (θ, p, η) η 𝑑 η

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/9906319

Formulas:

1-

α = 13^{h} 38^{m} {07.11}^{s}

2-

δ = - 80^{\circ} 29^{'} 48.2 "

3-

ℓ^{I I} = 304.942

4-

b^{I I} = - 17.8035

5-

F_{ν} \propto t^{- 0.85}

6-

F_{ν} \propto t^{- 1.3}

7-

F_{ν} \propto t^{- 1.8}

8-

F_{ν} \propto t^{- 2.5}

9-

S (ϕ) = \frac{\frac{I (ϕ) / I (ϕ + 90^{\circ})}{⟨ I_{u} (ϕ) / I_{u} (ϕ + 90^{\circ}) ⟩} - 1}{\frac{I (ϕ) / I (ϕ + 90^{\circ})}{⟨ I_{u} (ϕ) / I_{u} (ϕ + 90^{\circ}) ⟩} + 1}

10-

I (ϕ + 90^{\circ})

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0705.0203

Formulas:

1-

𝐮 = 𝐫_{k} - 𝐫_{i}

2-

𝐫_{i} \cdot 𝐫_{k} + 𝐫_{j} \cdot 𝐫_{k} < 𝐫_{k} \cdot 𝐫_{k} + 𝐫_{i} \cdot 𝐫_{j},

3-

𝐫_{i} \cdot 𝐫_{k} + 𝐫_{j} \cdot 𝐫_{k} = 𝐫_{k} \cdot 𝐫_{k} + 𝐫_{i} \cdot 𝐫_{j}

4-

𝐫_{i} \cdot 𝐫_{i} - 𝐫_{i} \cdot 𝐫_{j} - 𝐫_{i} \cdot 𝐫_{k} + 𝐫_{j} \cdot 𝐫_{k} < f_{c} (𝐫_{i} \cdot 𝐫_{i} + 𝐫_{k} \cdot 𝐫_{k} - 2 𝐫_{i} \cdot 𝐫_{k}) .

5-

𝐫_{j} \cdot 𝐫_{j} - 𝐫_{i} \cdot 𝐫_{j} + 𝐫_{i} \cdot 𝐫_{k} - 𝐫_{j} \cdot 𝐫_{k} < f_{c} (𝐫_{j} \cdot 𝐫_{j} + 𝐫_{k} \cdot 𝐫_{k} - 2 𝐫_{j} \cdot 𝐫_{k}) .

6-

𝐫_{i} \cdot 𝐫_{i} + 𝐫_{j} \cdot 𝐫_{j} - 2 𝐫_{i} \cdot 𝐫_{j} < f_{c} (𝐫_{i} \cdot 𝐫_{i} + 𝐫_{j} \cdot 𝐫_{j} + 2 𝐫_{k} \cdot 𝐫_{k} - 2 𝐫_{i} \cdot 𝐫_{k} - 2 𝐫_{j} \cdot 𝐫_{k}),

7-

\frac{1}{1 + 2 \sin^{2} (θ)}

8-

2 \sin^{- 1} (\frac{r_{s t}}{2 r_{c}}),

9-

r_{s t} = 0.9

10-

s_{c o m}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1403.6449

Formulas:

1-

L_{1}, \dots, L_{d}

2-

ℒ = {L_{1}, \dots, L_{d}}

3-

κ : J \to {1, 2, \dots, d}

4-

| {x \in J \cap l : κ (x) = j} | \leq C_{d} {| J |}^{1 / d}

5-

L_{1}, \dots, L_{d}

6-

ℒ = {L_{1}, \dots, L_{d}}

7-

κ : J \to {1, 2, \dots, d}

8-

| {x \in J \cap l : κ (x) = j} | \leq C_{d} {| J |}^{1 / d} .

9-

κ : J \to {1, 2, \dots, d}

10-

(m_{1}, \dots, m_{j - 1}, 0, m_{j + 1}, \dots m_{d})

Formulas (html):

Correct Categorie: math

Guessed Categorie: quant-ph

Result: incorrect

Run 11332253 (Agent494)