Run 10667649

Paper: https://arxiv.org/abs/astro-ph/0102468

Formulas:

1-

T_{x} \sim 3 \times 10^{6}

2-

L_{x} \sim 1.3 \times 10^{32}

3-

N_{H} \sim 6 \times 10^{21}

4-

\sim 2 \times 10^{- 3}

5-

T_{x} \sim 3 \times 10^{6}

6-

N_{H} \sim 6 \times 10^{21}

7-

F_{x} = 3.1 \times 10^{- 14}

8-

L_{x} = 1.3 \times 10^{32}

9-

3 \times 10^{6} K

10-

\sim 400 km s^{- 1}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: gr-qc

Result: incorrect

Paper: https://arxiv.org/abs/1811.06135

Formulas:

1-

X = {x_{1}, x_{2}, \dots, x_{n}}

2-

1 < n < + \infty

3-

U_{\min} \leq U \leq U_{\max}

4-

\frac{d U}{d K} < 0 .

5-

\frac{d U}{d I} > 0 .

6-

\frac{d U}{d K} = a U,

7-

\frac{d U}{d I} = b U,

8-

\ln U = a K + c_{1},

9-

\ln U = b I + c_{2},

10-

X = {x_{1}, x_{2}, \dots, x_{n}}

Formulas (html):

Correct Categorie: econ

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/9809419

Formulas:

1-

χ_{K P Z} = 1 / 2

2-

G (r) \sim r^{2 χ}

3-

χ_{D P D} \approx 0.63

4-

v \sim {(F - F_{c})}^{θ}

5-

ξ \sim {(F - F_{c})}^{- ν_{∥}}

6-

χ_{D P D}^{'} \approx 0.75

7-

χ_{K P Z} = 1 / 2

8-

χ \approx χ_{D P D}^{'}

9-

χ_{D P D}^{'}

10-

χ_{K P Z}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: hep-th

Result: incorrect

Paper: https://arxiv.org/abs/1108.3706

Formulas:

1-

P_{e 2 e}

2-

E T X_{P_{e 2 e}} = \sum_{l \in P_{e 2 e}} \frac{1}{(d_{f}^{(l)} \times d_{r}^{(l)})}

3-

i n v E T X_{P_{e 2 e}} = \sum_{l \in P_{e 2 e}} (d_{f}^{(l)} \times d_{r}^{(l)})

4-

M L_{P_{e 2 e}} = \prod_{l \in P_{e 2 e}} (d_{f}^{(l)} \times d_{r}^{(l)})

5-

(d_{f}^{(l)} \times d_{r}^{(l)})

6-

b y t e s

7-

P_{e 2 e}

8-

(d_{f}^{(l)} \times d_{r}^{(l)})

9-

i n v E T X

10-

i n v E T X

Formulas (html):

Correct Categorie: cs

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1212.2877

Formulas:

1-

(Δ S_{m})

2-

(Δ T_{a d})

3-

χ = g^{2} μ_{B}^{2} s (s + 1) / [3 k_{B} (T - θ)]

4-

B = 0, 1, 3

5-

Δ T_{a d}

6-

T_{C 1} ≃ 0.8

7-

T_{C 2} \approx 0.4

8-

M (T, B)

9-

S_{m} (T)

10-

S_{m} (T) = \int_{0}^{T} \frac{C_{m} (T)}{T} d T,

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0701352

Formulas:

1-

τ = L_{i r}

2-

L_{b o l}

3-

F_{1.2 m m}

4-

f_{t} (r) = σ (r) ε_{λ} B [T_{p} (r), λ] (\frac{2 π r d r}{D^{2}}),

5-

T_{p} (r)

6-

B [T_{p} (r), λ]

7-

ε_{λ} = 1.5 a / λ

8-

T_{p} (r) = 432 a_{μ m}^{- 0.2} {(L_{*} / L_{⊙})}^{0.2} {(r_{AU})}^{- 0.4}

9-

T_{p} (r) = 636 {(L_{*} / L_{⊙})}^{2 / 11} {(r_{AU})}^{- 4 / 11} {(T_{*} / T_{⊙})}^{3 / 11}

10-

σ = 0.1 - 1.5 \times 10^{- 3}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/1105.1013

Formulas:

1-

σ_{i j} - u_{a} δ_{i j}

2-

σ_{i j} - u_{a} δ_{i j}

3-

σ_{i j}^{'} = (σ_{i j} - u_{a} δ_{i j}) + χ (S_{r}) (u_{a} - u_{w}) δ_{i j}

4-

χ (S_{r})

5-

{\vec{F}}^{e x t, p}

6-

σ_{i j} = \frac{1}{V} \sum_{p ϵ \partial V} F_{i}^{e x t, p} x_{j}^{p}

7-

σ_{i j} = \frac{1}{V} \sum_{p = 1}^{N} \sum_{q = 1}^{N} F_{i}^{q, p} l_{j}^{q, p}

8-

{\vec{l}}^{q, p} = {\vec{x}}^{p} - {\vec{x}}^{q}

9-

{\vec{F}}_{c o n t}^{q, p}

10-

{\vec{F}}_{c a p}^{q, p}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cs

Result: incorrect

Paper: https://arxiv.org/abs/1609.00327

Formulas:

1-

n_{LFS} (ϕ)

2-

t_{obs} = 0.97 τ_{α}

3-

t_{obs} = 5 τ_{α}

4-

t_{obs} = 10 τ_{α}

5-

{0.888, 0.9573, 1.0, 1.043, 1.112}

6-

t_{obs} = 200 ≃ 10 τ_{α}

7-

F (t) = 1 / N ⟨ \exp (i 𝐤 \cdot [𝐫 (t + t^{'}) - 𝐫 (t^{'})]) ⟩

8-

| 𝐤 | = 2 π

9-

F (t) = c \exp [- {(t / τ_{α})}^{b}]

10-

τ_{α} \propto \exp [A / (ϕ_{0} - ϕ)]

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1504.03338

Formulas:

1-

{yr}^{- 1} {kpc}^{- 2}

2-

- 2 \ln L

3-

n^{2} \geq f i t - f i t_{\min}

4-

f i t - f i t_{\min} \leq 1

5-

f i t - f i t_{\min} \leq 4

6-

\log (T_{eff})

7-

e^{- 0.5 n^{2}}

8-

e^{- 0.5 \times 2^{2}}

9-

{yr}^{- 1} {kpc}^{- 2}

10-

Δ (\log t) = 0.1

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1905.00032

Formulas:

1-

(1.12 \pm 0.35) \times 10^{- 13}

2-

(6.4 \pm 0.6) \times 10^{10}

3-

(7.2 \pm 2.3) \times 10^{- 3}

4-

(2.1 \pm 0.7) \times 10^{- 12}

5-

r_{peri, out} = (3 - 10) a

6-

> 5.93 + 5.047 \times (G_{BP} - G_{RP})

7-

> 6 \times {(G_{BP} - G_{RP})}^{3} +

8-

- 21.77 \times {(G_{BP} - G_{RP})}^{2} +

9-

+ 27.91 \times (G_{BP} - G_{RP}) + 0.897

10-

(G_{BP} - G_{RP})

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1910.00133

Formulas:

1-

Ë † l m

2-

Ë † l m

3-

Ë † h i

4-

Ë † h i

5-

Ë † h i

6-

Ë † h i

7-

Ë † n q

8-

Ë † l m

9-

Ë † l m

10-

Ë † j k

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/0912.4461

Formulas:

1-

P G (4, 4)

2-

P G (4, 4)

3-

[[37, 27, 4]]

4-

[[39, 29, 4]]

5-

P G (r, q)

6-

G F (q)

7-

[[n, k, d]]

8-

[[n, 0, d]]

9-

P G (4, 4)

10-

A G (4, 4)

Formulas (html):

Correct Categorie: math

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/0910.3938

Formulas:

1-

L_{rad} = ϵ P_{sw}^{x},

2-

\log R_{H K}^{'}

3-

δ > - 30 °

4-

μ ≃ 0 \overset{''}{.} 5

5-

\frac{1}{{\bar{D}}^{2}} \equiv \sum_{i = 1}^{N} \frac{1}{D_{i}^{2}},

6-

\approx 100 mJy beam^{- 1}

7-

\approx 300 mJy beam^{- 1}

8-

P_{sw, kin} \propto n v^{3}

9-

P_{sw, mag} \propto v B^{2}

10-

σ \sim 3 mJy beam^{- 1}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

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

Formulas:

1-

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

2-

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

3-

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

4-

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

5-

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

6-

ϕ = \frac{2}{A} \ln t,

7-

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

8-

ρ + p = - {\dot{ϕ}}^{2} < 0

9-

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

10-

ρ_{p h} = \frac{12}{A^{4} t^{2}}

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/hep-th/9210029

Formulas:

1-

U_{t} = V_{x} + 3 U U_{x}

2-

A_{t} = A_{x x} + {(2 A^{2} - B)}_{x}

3-

V_{t} = U_{x x x} + V_{x} U + 2 U_{x} V

4-

B_{t} = - B_{x x} + {(4 A B)}_{x}

5-

U = j - \bar{j}

6-

V = {(j + \bar{j})}_{x} - \frac{1}{2} {(j + \bar{j})}^{2}

7-

A = ψ_{x} / 2 ψ

8-

B = ψ \bar{ψ}

9-

j_{t} = {(j_{x} + j^{2} - 2 j \bar{j})}_{x}

10-

ψ_{t} = ψ_{x x} - 2 ψ^{2} \bar{ψ}

Formulas (html):

Correct Categorie: hep-th

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/0905.4507

Formulas:

1-

N_{+}^{i n i}

2-

0 \leq ω (i) \leq 1

3-

ω (i) = ω_{f}

4-

ω (i) = ω_{o}

5-

S_{1}, S_{2}, S_{3}

6-

f_{σ} (i, j)

7-

f_{σ} (i, j) = 2

8-

σ (i) = σ (j)

9-

f_{σ} (i, j) = 1

10-

I_{K} = \frac{- \sum_{j \in S_{K}} f_{σ} (i, j) σ (i) σ (j)}{\sum_{j \in S_{K}} f_{σ} (i, j)}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: physics

Result: correct

Paper: https://arxiv.org/abs/0902.0136

Formulas:

1-

δ = 2.3 M_{f}

2-

H_{real} = M {[1 + 2 ν ({\hat{H}}_{eff} - 1)]}^{1 / 2}

3-

M \equiv m_{1} + m_{2}

4-

μ \equiv m_{1} m_{2} / M

5-

z_{3} = 2 ν (4 - 3 ν)

6-

{\hat{H}}_{eff} \equiv \sqrt{p_{r_{*}}^{2} + A (1 / r) (1 + p_{φ}^{2} / r^{2} + z_{3} p_{r_{*}}^{4} / r^{2})}

7-

A^{3 P N} (u) \equiv 1 - 2 u + 2 ν u^{3} + (94 / 3 - 41 π^{2} / 32) ν u^{4}

8-

A^{3 P N} (u)

9-

A (u; a_{5}, a_{6}, ν) \equiv P_{5}^{1} [A^{3 P N} (u) + ν a_{5} u^{5} + ν a_{6} u^{6}],

10-

ℱ_{φ} \equiv - \frac{1}{8 π Ω} \sum_{ℓ = 2}^{ℓ_{\max}} \sum_{m = 1}^{ℓ} {(m Ω)}^{2} {| R h_{ℓ m}^{(ϵ)} |}^{2} .

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: cs

Result: incorrect

Paper: https://arxiv.org/abs/physics/0304084

Formulas:

1-

l = s, p, d, f, g

2-

5 l_{j} - 5 l_{j^{'}}^{'}

3-

4 f_{j} - 5 l_{j^{'}}

4-

n s_{1 / 2}

5-

n p_{1 / 2}

6-

n p_{3 / 2}

7-

5 s_{1 / 2}

8-

n = 1, 2, and 3

9-

4 s^{2} 4 p^{6} 4 d^{10}

10-

5 s_{1 / 2} - 5 p_{j}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: physics

Result: correct

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

Formulas:

1-

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

2-

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

3-

V_{n} (r)

4-

W (r, T)

5-

⟨ W (r, T) ⟩

6-

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

7-

⟨ W (r, t) ⟩

8-

C_{l m} (r, T)

9-

l = 1, 2, 3

10-

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

Formulas (html):

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xref="S2.E1.m1.1.1.1.1.2.2.2.2.3.cmml"><mn id="S2.E1.m1.1.1.1.1.2.2.2.2.3a" xref="S2.E1.m1.1.1.1.1.2.2.2.2.3.cmml">0.5</mn></mpadded></mrow></mrow></mrow><mo id="S2.E1.m1.1.1.1.2">.</mo></mrow></math>, <math><mrow id="S2.p1.1.m1.1.2" xref="S2.p1.1.m1.1.2.cmml"><msub id="S2.p1.1.m1.1.2.2" xref="S2.p1.1.m1.1.2.2.cmml"><mi id="S2.p1.1.m1.1.2.2.2" xref="S2.p1.1.m1.1.2.2.2.cmml">E</mi><mi id="S2.p1.1.m1.1.2.2.3" xref="S2.p1.1.m1.1.2.2.3.cmml">stat</mi></msub><mo id="S2.p1.1.m1.1.2.1" xref="S2.p1.1.m1.1.2.1.cmml">∼</mo><mrow id="S2.p1.1.m1.1.2.3" xref="S2.p1.1.m1.1.2.3.cmml"><mrow id="S2.p1.1.m1.1.2.3.2" xref="S2.p1.1.m1.1.2.3.2.cmml"><mfrac id="S2.p1.1.m1.1.2.3.2.2" xref="S2.p1.1.m1.1.2.3.2.2.cmml"><mn id="S2.p1.1.m1.1.2.3.2.2.2" xref="S2.p1.1.m1.1.2.3.2.2.2.cmml">1</mn><mi id="S2.p1.1.m1.1.2.3.2.2.3" xref="S2.p1.1.m1.1.2.3.2.2.3.cmml">a</mi></mfrac><mo id="S2.p1.1.m1.1.2.3.2.1" xref="S2.p1.1.m1.1.2.3.2.1.cmml">⁢</mo><msup id="S2.p1.1.m1.1.2.3.2.3" xref="S2.p1.1.m1.1.2.3.2.3.cmml"><mi id="S2.p1.1.m1.1.2.3.2.3.2" xref="S2.p1.1.m1.1.2.3.2.3.2.cmml">e</mi><mrow id="S2.p1.1.m1.1.1.1.3" xref="S2.p1.1.m1.1.2.3.2.3.cmml"><mo stretchy="false" id="S2.p1.1.m1.1.1.1.3.1" xref="S2.p1.1.m1.1.2.3.2.3.cmml">(</mo><mn id="S2.p1.1.m1.1.1.1.1" xref="S2.p1.1.m1.1.1.1.1.cmml">1</mn><mo stretchy="false" id="S2.p1.1.m1.1.1.1.3.2" xref="S2.p1.1.m1.1.2.3.2.3.cmml">)</mo></mrow></msup><mo id="S2.p1.1.m1.1.2.3.2.1a" xref="S2.p1.1.m1.1.2.3.2.1.cmml">⁢</mo><msubsup id="S2.p1.1.m1.1.2.3.2.4" xref="S2.p1.1.m1.1.2.3.2.4.cmml"><mi id="S2.p1.1.m1.1.2.3.2.4.2.2" xref="S2.p1.1.m1.1.2.3.2.4.2.2.cmml">g</mi><mn id="S2.p1.1.m1.1.2.3.2.4.2.3" xref="S2.p1.1.m1.1.2.3.2.4.2.3.cmml">0</mn><mn id="S2.p1.1.m1.1.2.3.2.4.3" xref="S2.p1.1.m1.1.2.3.2.4.3.cmml">2</mn></msubsup></mrow><mo id="S2.p1.1.m1.1.2.3.1" xref="S2.p1.1.m1.1.2.3.1.cmml">+</mo><mi mathvariant="normal" id="S2.p1.1.m1.1.2.3.3" xref="S2.p1.1.m1.1.2.3.3.cmml">…</mi></mrow></mrow></math>, <math><mrow id="S2.p1.3.m3.1.2" xref="S2.p1.3.m3.1.2.cmml"><msub id="S2.p1.3.m3.1.2.2" xref="S2.p1.3.m3.1.2.2.cmml"><mi id="S2.p1.3.m3.1.2.2.2" xref="S2.p1.3.m3.1.2.2.2.cmml">V</mi><mi id="S2.p1.3.m3.1.2.2.3" xref="S2.p1.3.m3.1.2.2.3.cmml">n</mi></msub><mo id="S2.p1.3.m3.1.2.1" xref="S2.p1.3.m3.1.2.1.cmml">⁢</mo><mrow id="S2.p1.3.m3.1.2.3.2" xref="S2.p1.3.m3.1.2.cmml"><mo stretchy="false" id="S2.p1.3.m3.1.2.3.2.1" xref="S2.p1.3.m3.1.2.cmml">(</mo><mi id="S2.p1.3.m3.1.1" xref="S2.p1.3.m3.1.1.cmml">r</mi><mo stretchy="false" id="S2.p1.3.m3.1.2.3.2.2" xref="S2.p1.3.m3.1.2.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S2.p1.5.m5.2.3" xref="S2.p1.5.m5.2.3.cmml"><mi id="S2.p1.5.m5.2.3.2" xref="S2.p1.5.m5.2.3.2.cmml">W</mi><mo id="S2.p1.5.m5.2.3.1" xref="S2.p1.5.m5.2.3.1.cmml">⁢</mo><mrow id="S2.p1.5.m5.2.3.3.2" xref="S2.p1.5.m5.2.3.3.1.cmml"><mo stretchy="false" id="S2.p1.5.m5.2.3.3.2.1" xref="S2.p1.5.m5.2.3.3.1.cmml">(</mo><mi id="S2.p1.5.m5.1.1" xref="S2.p1.5.m5.1.1.cmml">r</mi><mo id="S2.p1.5.m5.2.3.3.2.2" xref="S2.p1.5.m5.2.3.3.1.cmml">,</mo><mi id="S2.p1.5.m5.2.2" xref="S2.p1.5.m5.2.2.cmml">T</mi><mo stretchy="false" id="S2.p1.5.m5.2.3.3.2.3" xref="S2.p1.5.m5.2.3.3.1.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S2.E2.m1.3.3.1" xref="S2.E2.m1.3.3.2.cmml"><mo id="S2.E2.m1.3.3.1.2" xref="S2.E2.m1.3.3.2.1.cmml">⟨</mo><mrow id="S2.E2.m1.3.3.1.1" xref="S2.E2.m1.3.3.1.1.cmml"><mi id="S2.E2.m1.3.3.1.1.2" xref="S2.E2.m1.3.3.1.1.2.cmml">W</mi><mo id="S2.E2.m1.3.3.1.1.1" xref="S2.E2.m1.3.3.1.1.1.cmml">⁢</mo><mrow id="S2.E2.m1.3.3.1.1.3.2" xref="S2.E2.m1.3.3.1.1.3.1.cmml"><mo stretchy="false" id="S2.E2.m1.3.3.1.1.3.2.1" xref="S2.E2.m1.3.3.1.1.3.1.cmml">(</mo><mi id="S2.E2.m1.1.1" xref="S2.E2.m1.1.1.cmml">r</mi><mo id="S2.E2.m1.3.3.1.1.3.2.2" xref="S2.E2.m1.3.3.1.1.3.1.cmml">,</mo><mi id="S2.E2.m1.2.2" xref="S2.E2.m1.2.2.cmml">T</mi><mo stretchy="false" id="S2.E2.m1.3.3.1.1.3.2.3" xref="S2.E2.m1.3.3.1.1.3.1.cmml">)</mo></mrow></mrow><mo id="S2.E2.m1.3.3.1.3" xref="S2.E2.m1.3.3.2.1.cmml">⟩</mo></mrow></math>, <math><mrow id="S2.E2.m3.4.4.1"><mrow id="S2.E2.m3.4.4.1.1.1" xref="S2.E2.m3.4.4.1.1.2.cmml"><mrow id="S2.E2.m3.4.4.1.1.1.1" xref="S2.E2.m3.4.4.1.1.1.1.cmml"><mstyle displaystyle="true" id="S2.E2.m3.4.4.1.1.1.1.1" xref="S2.E2.m3.4.4.1.1.1.1.1.cmml"><munder id="S2.E2.m3.4.4.1.1.1.1.1a" xref="S2.E2.m3.4.4.1.1.1.1.1.cmml"><mo largeop="true" movablelimits="false" symmetric="true" id="S2.E2.m3.4.4.1.1.1.1.1.2" xref="S2.E2.m3.4.4.1.1.1.1.1.2.cmml">∑</mo><mi id="S2.E2.m3.4.4.1.1.1.1.1.3" xref="S2.E2.m3.4.4.1.1.1.1.1.3.cmml">n</mi></munder></mstyle><mrow id="S2.E2.m3.4.4.1.1.1.1.2" xref="S2.E2.m3.4.4.1.1.1.1.2.cmml"><msub id="S2.E2.m3.4.4.1.1.1.1.2.2" xref="S2.E2.m3.4.4.1.1.1.1.2.2.cmml"><mi id="S2.E2.m3.4.4.1.1.1.1.2.2.2" xref="S2.E2.m3.4.4.1.1.1.1.2.2.2.cmml">c</mi><mi id="S2.E2.m3.4.4.1.1.1.1.2.2.3" xref="S2.E2.m3.4.4.1.1.1.1.2.2.3.cmml">n</mi></msub><mo id="S2.E2.m3.4.4.1.1.1.1.2.1" xref="S2.E2.m3.4.4.1.1.1.1.2.1.cmml">⁢</mo><msubsup id="S2.E2.m3.4.4.1.1.1.1.2.3" xref="S2.E2.m3.4.4.1.1.1.1.2.3.cmml"><mi id="S2.E2.m3.4.4.1.1.1.1.2.3.2.2" xref="S2.E2.m3.4.4.1.1.1.1.2.3.2.2.cmml">c</mi><mi id="S2.E2.m3.4.4.1.1.1.1.2.3.2.3" xref="S2.E2.m3.4.4.1.1.1.1.2.3.2.3.cmml">n</mi><mo id="S2.E2.m3.4.4.1.1.1.1.2.3.3" xref="S2.E2.m3.4.4.1.1.1.1.2.3.3.cmml">*</mo></msubsup><mo id="S2.E2.m3.4.4.1.1.1.1.2.1a" xref="S2.E2.m3.4.4.1.1.1.1.2.1.cmml">⁢</mo><msup id="S2.E2.m3.4.4.1.1.1.1.2.4" xref="S2.E2.m3.4.4.1.1.1.1.2.4.cmml"><mi mathvariant="normal" id="S2.E2.m3.4.4.1.1.1.1.2.4.2" xref="S2.E2.m3.4.4.1.1.1.1.2.4.2.cmml">e</mi><mrow id="S2.E2.m3.3.3.2" xref="S2.E2.m3.3.3.2.cmml"><mo id="S2.E2.m3.3.3.2.3" xref="S2.E2.m3.3.3.2.3.cmml">-</mo><mrow id="S2.E2.m3.3.3.2.2" xref="S2.E2.m3.3.3.2.2.cmml"><msub id="S2.E2.m3.3.3.2.2.3" xref="S2.E2.m3.3.3.2.2.3.cmml"><mi id="S2.E2.m3.3.3.2.2.3.2" xref="S2.E2.m3.3.3.2.2.3.2.cmml">V</mi><mi id="S2.E2.m3.3.3.2.2.3.3" xref="S2.E2.m3.3.3.2.2.3.3.cmml">n</mi></msub><mo id="S2.E2.m3.3.3.2.2.2" xref="S2.E2.m3.3.3.2.2.2.cmml">⁢</mo><mrow id="S2.E2.m3.3.3.2.2.4.2" xref="S2.E2.m3.3.3.2.2.cmml"><mo stretchy="false" id="S2.E2.m3.3.3.2.2.4.2.1" xref="S2.E2.m3.3.3.2.2.cmml">(</mo><mi id="S2.E2.m3.2.2.1.1" xref="S2.E2.m3.2.2.1.1.cmml">r</mi><mo stretchy="false" id="S2.E2.m3.3.3.2.2.4.2.2" xref="S2.E2.m3.3.3.2.2.cmml">)</mo></mrow><mo id="S2.E2.m3.3.3.2.2.2a" xref="S2.E2.m3.3.3.2.2.2.cmml">⁢</mo><mrow id="S2.E2.m3.3.3.2.2.1.1" xref="S2.E2.m3.3.3.2.2.1.1.1.cmml"><mo stretchy="false" id="S2.E2.m3.3.3.2.2.1.1.2" xref="S2.E2.m3.3.3.2.2.1.1.1.cmml">(</mo><mrow id="S2.E2.m3.3.3.2.2.1.1.1" xref="S2.E2.m3.3.3.2.2.1.1.1.cmml"><mi id="S2.E2.m3.3.3.2.2.1.1.1.2" xref="S2.E2.m3.3.3.2.2.1.1.1.2.cmml">T</mi><mo id="S2.E2.m3.3.3.2.2.1.1.1.1" xref="S2.E2.m3.3.3.2.2.1.1.1.1.cmml">-</mo><mrow id="S2.E2.m3.3.3.2.2.1.1.1.3" xref="S2.E2.m3.3.3.2.2.1.1.1.3.cmml"><mn id="S2.E2.m3.3.3.2.2.1.1.1.3.2" xref="S2.E2.m3.3.3.2.2.1.1.1.3.2.cmml">2</mn><mo id="S2.E2.m3.3.3.2.2.1.1.1.3.1" xref="S2.E2.m3.3.3.2.2.1.1.1.3.1.cmml">⁢</mo><mi id="S2.E2.m3.3.3.2.2.1.1.1.3.3" xref="S2.E2.m3.3.3.2.2.1.1.1.3.3.cmml">a</mi></mrow></mrow><mo stretchy="false" id="S2.E2.m3.3.3.2.2.1.1.3" xref="S2.E2.m3.3.3.2.2.1.1.1.cmml">)</mo></mrow></mrow></mrow></msup></mrow></mrow><mo mathvariant="italic" separator="true" id="S2.E2.m3.4.4.1.1.1.2" xref="S2.E2.m3.4.4.1.1.2.cmml"> </mo><mpadded width="+1.7pt" id="S2.E2.m3.1.1.1a" xref="S2.E2.m3.1.1.1ad.cmml"><mrow id="S2.E2.m3.1.1.1aa" xref="S2.E2.m3.1.1.1ad.cmml"><mtext id="S2.E2.m3.1.1.1ab" xref="S2.E2.m3.1.1.1ad.cmml">(with </mtext><mrow id="S2.E2.m3.1.1.1.m1.1.1" xref="S2.E2.m3.1.1.1.m1.1.1.cmml"><msub id="S2.E2.m3.1.1.1.m1.1.1.2" xref="S2.E2.m3.1.1.1.m1.1.1.2.cmml"><mi id="S2.E2.m3.1.1.1.m1.1.1.2.2" xref="S2.E2.m3.1.1.1.m1.1.1.2.2.cmml">N</mi><mi id="S2.E2.m3.1.1.1.m1.1.1.2.3" xref="S2.E2.m3.1.1.1.m1.1.1.2.3.cmml">t</mi></msub><mo id="S2.E2.m3.1.1.1.m1.1.1.1" xref="S2.E2.m3.1.1.1.m1.1.1.1.cmml">→</mo><mi mathvariant="normal" id="S2.E2.m3.1.1.1.m1.1.1.3" xref="S2.E2.m3.1.1.1.m1.1.1.3.cmml">∞</mi></mrow><mtext id="S2.E2.m3.1.1.1ac" xref="S2.E2.m3.1.1.1ad.cmml"> time-slices)</mtext></mrow></mpadded></mrow><mo id="S2.E2.m3.4.4.1.2">.</mo></mrow></math>, <math><mrow id="S2.E3.m1.3.3.1" xref="S2.E3.m1.3.3.2.cmml"><mo id="S2.E3.m1.3.3.1.2" xref="S2.E3.m1.3.3.2.1.cmml">⟨</mo><mrow id="S2.E3.m1.3.3.1.1" xref="S2.E3.m1.3.3.1.1.cmml"><mi id="S2.E3.m1.3.3.1.1.2" xref="S2.E3.m1.3.3.1.1.2.cmml">W</mi><mo id="S2.E3.m1.3.3.1.1.1" xref="S2.E3.m1.3.3.1.1.1.cmml">⁢</mo><mrow id="S2.E3.m1.3.3.1.1.3.2" xref="S2.E3.m1.3.3.1.1.3.1.cmml"><mo stretchy="false" id="S2.E3.m1.3.3.1.1.3.2.1" xref="S2.E3.m1.3.3.1.1.3.1.cmml">(</mo><mi id="S2.E3.m1.1.1" xref="S2.E3.m1.1.1.cmml">r</mi><mo id="S2.E3.m1.3.3.1.1.3.2.2" xref="S2.E3.m1.3.3.1.1.3.1.cmml">,</mo><mi id="S2.E3.m1.2.2" xref="S2.E3.m1.2.2.cmml">t</mi><mo stretchy="false" id="S2.E3.m1.3.3.1.1.3.2.3" xref="S2.E3.m1.3.3.1.1.3.1.cmml">)</mo></mrow></mrow><mo id="S2.E3.m1.3.3.1.3" xref="S2.E3.m1.3.3.2.1.cmml">⟩</mo></mrow></math>, <math><mrow id="S2.E3.m3.2.3" xref="S2.E3.m3.2.3.cmml"><msub id="S2.E3.m3.2.3.2" xref="S2.E3.m3.2.3.2.cmml"><mi id="S2.E3.m3.2.3.2.2" xref="S2.E3.m3.2.3.2.2.cmml">C</mi><mrow id="S2.E3.m3.2.3.2.3" xref="S2.E3.m3.2.3.2.3.cmml"><mi id="S2.E3.m3.2.3.2.3.2" xref="S2.E3.m3.2.3.2.3.2.cmml">l</mi><mo id="S2.E3.m3.2.3.2.3.1" xref="S2.E3.m3.2.3.2.3.1.cmml">⁢</mo><mi id="S2.E3.m3.2.3.2.3.3" xref="S2.E3.m3.2.3.2.3.3.cmml">m</mi></mrow></msub><mo id="S2.E3.m3.2.3.1" xref="S2.E3.m3.2.3.1.cmml">⁢</mo><mrow id="S2.E3.m3.2.3.3.2" xref="S2.E3.m3.2.3.3.1.cmml"><mo stretchy="false" id="S2.E3.m3.2.3.3.2.1" xref="S2.E3.m3.2.3.3.1.cmml">(</mo><mi id="S2.E3.m3.1.1" xref="S2.E3.m3.1.1.cmml">r</mi><mo id="S2.E3.m3.2.3.3.2.2" xref="S2.E3.m3.2.3.3.1.cmml">,</mo><mi id="S2.E3.m3.2.2" xref="S2.E3.m3.2.2.cmml">T</mi><mo stretchy="false" id="S2.E3.m3.2.3.3.2.3" xref="S2.E3.m3.2.3.3.1.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S2.p1.10.m1.3.4" xref="S2.p1.10.m1.3.4.cmml"><mi id="S2.p1.10.m1.3.4.2" xref="S2.p1.10.m1.3.4.2.cmml">l</mi><mo id="S2.p1.10.m1.3.4.1" xref="S2.p1.10.m1.3.4.1.cmml">=</mo><mrow id="S2.p1.10.m1.3.4.3.2" xref="S2.p1.10.m1.3.4.3.1.cmml"><mn id="S2.p1.10.m1.1.1" xref="S2.p1.10.m1.1.1.cmml">1</mn><mo id="S2.p1.10.m1.3.4.3.2.1" xref="S2.p1.10.m1.3.4.3.1.cmml">,</mo><mn id="S2.p1.10.m1.2.2" xref="S2.p1.10.m1.2.2.cmml">2</mn><mo id="S2.p1.10.m1.3.4.3.2.2" xref="S2.p1.10.m1.3.4.3.1.cmml">,</mo><mn id="S2.p1.10.m1.3.3" xref="S2.p1.10.m1.3.3.cmml">3</mn></mrow></mrow></math>, <math><mrow id="S2.p2.1.m1.1.1" xref="S2.p2.1.m1.1.1.cmml"><mrow id="S2.p2.1.m1.1.1.2" xref="S2.p2.1.m1.1.1.2.cmml"><msub id="S2.p2.1.m1.1.1.2.2" xref="S2.p2.1.m1.1.1.2.2.cmml"><mi id="S2.p2.1.m1.1.1.2.2.2" xref="S2.p2.1.m1.1.1.2.2.2.cmml">r</mi><mn id="S2.p2.1.m1.1.1.2.2.3" xref="S2.p2.1.m1.1.1.2.2.3.cmml">0</mn></msub><mo id="S2.p2.1.m1.1.1.2.1" xref="S2.p2.1.m1.1.1.2.1.cmml">⁢</mo><msub id="S2.p2.1.m1.1.1.2.3" xref="S2.p2.1.m1.1.1.2.3.cmml"><mi id="S2.p2.1.m1.1.1.2.3.2" xref="S2.p2.1.m1.1.1.2.3.2.cmml">M</mi><mi id="S2.p2.1.m1.1.1.2.3.3" xref="S2.p2.1.m1.1.1.2.3.3.cmml">PS</mi></msub></mrow><mo id="S2.p2.1.m1.1.1.1" xref="S2.p2.1.m1.1.1.1.cmml">≈</mo><mrow id="S2.p2.1.m1.1.1.3" xref="S2.p2.1.m1.1.1.3.cmml"><mn id="S2.p2.1.m1.1.1.3.2" xref="S2.p2.1.m1.1.1.3.2.cmml">0.62</mn><mo id="S2.p2.1.m1.1.1.3.1" xref="S2.p2.1.m1.1.1.3.1.cmml">⁢</mo><mi mathvariant="normal" id="S2.p2.1.m1.1.1.3.3" xref="S2.p2.1.m1.1.1.3.3.cmml">…</mi><mo id="S2.p2.1.m1.1.1.3.1a" xref="S2.p2.1.m1.1.1.3.1.cmml">⁢</mo><mn id="S2.p2.1.m1.1.1.3.4" xref="S2.p2.1.m1.1.1.3.4.cmml">0.64</mn></mrow></mrow></math>

Correct Categorie: hep-lat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1010.4350

Formulas:

1-

{| 0 ⟩, | 1 ⟩}

2-

| ψ ⟩ = | ψ_{1} ⟩ \otimes | ψ_{2} ⟩

3-

U_{s w a p} {| ψ_{1} ⟩}_{q_{A_{1}}} {| ψ_{2} ⟩}_{q_{A_{2}}} = {| ψ_{2} ⟩}_{q_{B_{1}}} {| ψ_{1} ⟩}_{q_{B_{2}}} .

4-

| Φ^{+} ⟩ = (| 00 ⟩ + | 11 ⟩) / \sqrt{2} .

5-

i + k, j + l

6-

i + k, j + l

7-

i + k, j + l

8-

X^{i + k} Z^{j + l}

9-

{| Φ^{i, j} ⟩ ⟨ Φ^{i, j} |}_{i, j}

10-

| Φ^{i, j} ⟩ = Z^{j} X^{i} | Φ^{+} ⟩

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: hep-th

Result: incorrect

Paper: https://arxiv.org/abs/0812.4387

Formulas:

1-

d_{\pm}^{†}, d_{\pm}

2-

J_{x} \equiv (d_{-}^{†} d_{-} - d_{+}^{†} d_{+}) / 2

3-

J_{y} \equiv i (d_{-}^{†} d_{+} - d_{+}^{†} d_{-}) / 2

4-

J_{z} \equiv (d_{+}^{†} d_{-} + d_{-}^{†} d_{+}) / 2

5-

\hat{H} = 2 [2 Λ (N - 1) + \frac{Ω}{2}] J_{z} + 2 (κ - η) J_{x}^{2} + 4 η J_{z}^{2} .

6-

η = κ ϵ^{2}, Λ = κ ϵ^{\frac{3}{2}}

7-

ϵ = ⟨ u_{+} | u_{-} ⟩

8-

Ω^{^{'}} \equiv 2 [2 Λ (N - 1) + Ω / 2]

9-

s u (2)

10-

S U (2)

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0107249

Formulas:

1-

\frac{M_{I C M}^{F e}}{M_{*}^{F e}} = \frac{Z_{I C M}^{F e} M_{I C M}}{Z_{*}^{F e} M_{*}} = 1.65 h^{- 3 / 2}

2-

M_{I C M}^{F e} \propto L_{V}^{E + S 0}

3-

M_{g a s}^{e j}

4-

M_{F e}^{e j}

5-

M_{F e}^{I C M}

6-

\frac{d N}{d \log M} \propto M^{- x} e x p (- \frac{M_{s}}{M})

7-

M_{p} \sim \frac{M_{s}}{x}

8-

M_{p} \propto T^{2} ρ^{- \frac{1}{2}}

9-

M_{p} = 0.2 M_{⊙} {(\frac{T}{10 K})}^{2} {(\frac{n}{1000 K})}^{- \frac{1}{2}} {(\frac{Σ_{g}}{2.5 k m s e c^{- 1}})}^{- 1}

10-

z_{f o r}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: hep-lat

Result: incorrect

Paper: https://arxiv.org/abs/1611.00931

Formulas:

1-

f : 𝒰 \times 𝒜 \to 𝒱

2-

IND (𝒫) = {(x_{m}, x_{n}) \in 𝒰^{2} | \forall a \in 𝒫, f (x_{m}, a) = f (x_{n}, a)},

3-

𝒰 / IND (𝒫) = {{[x_{m}]}_{𝒫} | x_{m} \in 𝒰} .

4-

\underline{𝒫} (𝒳) = \cup {[x_{m}] | [x_{m}] \subseteq 𝒳},

5-

\bar{𝒫} (𝒳) = \cup {[x_{m}] | [x_{m}] \cap 𝒳 \neq ϕ} .

6-

\underline{𝒫} (𝒳)

7-

\bar{𝒫} (𝒳)

8-

\bar{𝒫} (𝒳)

9-

\underline{𝒫} (𝒳)

10-

\underline{𝒫} (𝒳)

Formulas (html):

Correct Categorie: cs

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/physics/0510124

Formulas:

1-

E = m c^{2}

2-

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

3-

L = L_{0} \sqrt{1 - \frac{v^{2}}{c^{2}}}

4-

\sqrt{1 - \frac{v^{2}}{c^{2}}}

5-

γ (t - \frac{v}{c^{2}} x)

6-

γ (x - v t)

7-

γ = \frac{1}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}

8-

ρ (ν, T) = c_{1} ν^{3} e^{\frac{c_{2} ν}{T}}

9-

ρ (ν, T) = \frac{8 π ν^{2}}{c^{3}} k T

10-

h ν, 2 h ν, 3 h ν,

Formulas (html):

Correct Categorie: physics

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1303.4995

Formulas:

1-

n (H_{2})

2-

E = \frac{ϵ M (H_{2})}{160} \times 10^{51} e r g s

3-

Σ_{t h} = 100

4-

M_{V} (t)

5-

M_{V 0} (t)

6-

M_{V} (t)

7-

M_{V 0} (t)

8-

M_{V} (t)

9-

M_{V 0} (t)

10-

2 \times 10^{6} M_{⊙}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: gr-qc

Result: incorrect

Paper: https://arxiv.org/abs/1510.04557

Formulas:

1-

s c c m

2-

s c c m

3-

f (x, y)

4-

f (x, y)

5-

f (x, y)

6-

| \nabla f (x, y) |

7-

\frac{\partial f}{\partial x}

8-

\frac{\partial f}{\partial y}

9-

f (x, y)

10-

△ f (x, y) = \frac{\partial^{2} f (x, y)}{\partial x^{2}} + \frac{\partial^{2} f (x, y)}{\partial y^{2}} .

Formulas (html):

Correct Categorie: physics

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1501.06878

Formulas:

1-

k δ (u)

2-

l δ (v)

3-

u = 0, v = 0

4-

Λ = - 6 k l

5-

d s^{2} = - {(1 + k u_{+})}^{2} d x^{2} - {(1 - k u_{+})}^{2} d y^{2} + 2 d u d v,

6-

u_{+} = u ϑ (u)

7-

ϑ (u) = 1

8-

ϑ (u) = 0

9-

ϑ^{1} = (1 + k u_{+}) d x, ϑ^{2} = (1 - k u_{+}) d y, ϑ^{3} = d v, ϑ^{4} = d u

10-

Ψ_{4} = - k δ (u) .

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: hep-th

Result: incorrect

Paper: https://arxiv.org/abs/1301.1684

Formulas:

1-

M ≳ 10^{15} M_{⊙}

2-

ρ (r) / σ^{3} (r)

3-

Σ (R) = \int 𝑑 x_{∥} ρ (x_{∥}, R),

4-

𝐫 = (x_{∥}, R)

5-

M ≳ 10^{15} M_{⊙}

6-

r_{v i r}

7-

M_{v i r}

8-

(M p c h^{- 1})

9-

(10^{15} M_{⊙} h^{- 1})

10-

ρ (r) = \frac{ρ_{s}}{(r / r_{s}) {(1 + r / r_{s})}^{2}},

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1904.06873

Formulas:

1-

0.809 M_{⊙} \leq M_{ZAMS} \leq 0.83 M_{⊙}

2-

0.45 \leq η_{R} \leq 0.55

3-

M_{ZAMS} = 0.811 M_{⊙}

4-

{⟨ Π ⟩}_{0} = 0.79

5-

M \approx 0.6 M_{⊙}

6-

6000 K ≲ T_{eff} ≲ 7600 K

7-

{⟨ Π ⟩}_{RRab} < 0.6

8-

{⟨ Π ⟩}_{RRc} < 0.35

9-

{⟨ Π ⟩}_{RRab} > 0.6

10-

{⟨ Π ⟩}_{RRc} > 0.35

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/math/9804124

Formulas:

1-

det [(\binom{i + j}{i}) {(\binom{2 n - i - j}{n - i})}_{0 \leq i, j \leq n}] = \frac{{(2 n + 1)!}^{n + 1}}{(2 n + 1)!!},

2-

a!! := 0! \cdot 1! \cdot 2! \dots a!

3-

a! := 1 \cdot 2 \dots a

4-

m = n, a = b = 0

5-

det [(\binom{i + j + a + b}{i + a}) {(\binom{2 n - i - j - a - b}{n - i - a})}_{0 \leq i, j \leq m}] =

6-

\frac{(a + b)! {(2 n + 1)!}^{m + 1} (2 n - m)!! m!! (m + a + b)!! (2 n - m - a - b)!! a!! b!! (n - m - a - 1)!! (n - m - b - 1)!!}{a! b! (2 n + 1)!! (n - a)!! (n - b)!! (m + a)!! (m + b)!! (a + b)!! (2 n - 2 m - a - b - 1)!!},

7-

(R a b b i t)

8-

A_{r} (k, l)

9-

det A = \frac{det A_{n - 1} (1, 1) det A_{n - 1} (2, 2) - det A_{n - 1} (1, 2) det A_{n - 1} (2, 1)}{det A_{n - 2} (2, 2)} .

10-

(L e w i s)

Formulas (html):

Correct Categorie: math

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/quant-ph/0604083

Formulas:

1-

i ℏ \frac{\partial \hat{O} (t)}{\partial t} = [\hat{O} (t), \hat{H}],

2-

i ℏ \frac{\partial | ψ (t) ⟩}{\partial t} = \hat{H} | ψ (t) ⟩,

3-

\hat{H} (\vec{x}) = - \frac{ℏ^{2}}{2 m} \nabla_{\vec{x}}^{2} + U (\vec{x}),

4-

\nabla_{\vec{x}}^{2} = \partial^{2} / \partial x_{1}^{2} + \partial^{2} / \partial x_{2}^{2} + \partial^{2} / \partial x_{3}^{2},

5-

U (\vec{x})

6-

\vec{x} = (x_{1}, x_{2}, x_{3}) \in ℝ^{3} .

7-

i ℏ \frac{\partial ψ (\vec{x}, t)}{\partial t} = \hat{H} (\vec{x}) ψ (\vec{x}, t) = - \frac{ℏ^{2}}{2 m} \nabla_{\vec{x}}^{2} ψ (\vec{x}, t) + U (\vec{x}) ψ (\vec{x}, t) .

8-

ψ (\vec{x}, t)

9-

φ (\vec{x}, t)

10-

\begin{matrix} i ℏ \frac{\partial (ψ (\vec{x}, t) φ^{*} (\vec{y}, t))}{\partial t} & = & i ℏ \frac{\partial ψ (\vec{x}, t)}{\partial t} φ^{*} (\vec{y}, t) + i ℏ \frac{\partial φ^{*} (\vec{y}, t)}{\partial t} ψ (\vec{x}, t) \\ = & [\hat{H} (\vec{x}) ψ (\vec{x}, t)] φ^{*} (\vec{y}, t) \\ - {[\hat{H} (\vec{y}) φ (\vec{y}, t)]}^{*} ψ (\vec{x}, t) \\ = & (\hat{H} (\vec{x}) - \hat{H} (\vec{y})) (ψ (\vec{x}, t) φ^{*} (\vec{y}, t)) . \end{matrix}

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/1402.5908

Formulas:

1-

n_{QD} \approx 8 \cdot 10^{9}

2-

ϵ_{m} := E_{m} - E_{m - 1}

3-

Δ E = e \frac{d_{tunn}}{d_{tot}} Δ V_{G} = \frac{e}{λ} Δ V_{G}

4-

λ = \frac{d_{tot}}{d_{tunn}} = 7

5-

Δ σ = | σ (0) - σ (\infty) |

6-

\frac{Δ σ}{Δ V_{G}} = \frac{Δ n e μ}{\frac{Δ E}{e λ}} = λ e^{2} μ \frac{Δ n}{Δ E} = λ e^{2} μ D (E),

7-

\bar{ν} = (ν_{1} + 1 / ν_{2}) / 2

8-

Δ E \sim 1.4 meV

9-

V_{G} = - 0.67 V

10-

τ_{0 \to 1} = 2.3

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: hep-th

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0311586

Formulas:

1-

p_{γ} (U)

2-

\exp [- γ U]

3-

I = \int 𝑑 𝐱 p_{θ} (𝐱) {\frac{\frac{\partial p_{θ} (𝐱)}{\partial θ}}{p_{θ} (𝐱)}}^{2} = ⟨ {[\frac{1}{p_{θ}} \frac{\partial p_{θ}}{\partial θ}]}^{2} ⟩ .

4-

p_{θ} (𝐱)

5-

\tilde{θ} = \tilde{θ} (𝐱)

6-

\tilde{θ} (𝐱)

7-

I e^{2} = 1

8-

⟨ \tilde{θ} (𝐱) ⟩ = θ

9-

I e^{2} \geq 1,

10-

P_{θ} (𝐱) = p_{θ}^{q} (𝐱) / \int 𝑑 𝐱 p_{θ}^{q} (𝐱)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0011425

Formulas:

1-

{⟨ B ⟩}_{x} = ⟨ B ⟩ \cos θ

2-

{⟨ B ⟩}_{y} = 0

3-

{⟨ B ⟩}_{z} = ⟨ B ⟩ \sin θ

4-

⟨ B ⟩ / δ B ≪ 1

5-

δ B_{x} = δ B \cos φ

6-

δ B_{y} = δ B \sin φ \cos ψ

7-

δ B_{z} = δ B \sin φ \sin ψ

8-

[- 1, 1]

9-

[0, 2 π)

10-

𝐁 = 𝜹 𝐁 + ⟨ 𝐁 ⟩

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: gr-qc

Result: incorrect

Paper: https://arxiv.org/abs/1508.02996

Formulas:

1-

a s d i m (X) \leq n

2-

a s d i m (Y) = 0

3-

(X, ℒ 𝒮 𝒮_{X})

4-

𝒱 = ⋃_{i = 1}^{n + 1} 𝒱_{i}

5-

s t (𝒱_{i}, 𝒰)

6-

i = 1, 2, \dots, n

7-

U_{1}, U_{2}, \dots, U_{n} \in 𝒰

8-

s t^{n} (f (U_{i}), f (𝒱)) \supset V

9-

s t (U, 𝒰) = \cup {V \in 𝒰 : V \cap U \neq \emptyset}

10-

𝒱_{1}, 𝒱_{2} \subset 2^{X}

Formulas (html):

Correct Categorie: math

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1807.09689

Formulas:

1-

ω (θ, z)

2-

(r, θ, z)

3-

θ = θ (x, y)

4-

z = z (x, y)

5-

\bar{ω} (x, y)

6-

h = (24 \pm 5) μ m

7-

R = (4.0 \pm 0.1) cm

8-

a = (0.5 \pm 0.1) cm

9-

d = (1.50 \pm 0.05) mm

10-

L_{c} = (11.5 \pm 0.6) cm

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/hep-th/0206194

Formulas:

1-

A d S_{5} \times S^{5}

2-

g = d V (d U + α d V + β_{i} d Y^{i}) + C_{i j} d Y^{i} d Y^{j},

3-

V = Y^{i} = 0

4-

U = u, V = Ω^{2} v, Y^{i} = Ω y^{i},

5-

g_{Ω} = Ω^{- 2} g

6-

\bar{g} \equiv lim_{Ω \to 0} g_{Ω}

7-

δ B_{k - 1} = d Λ_{k - 2}

8-

H_{k} = d B_{k - 1}

9-

H_{Ω} = Ω^{- k + 1} H

10-

\bar{H} \equiv {lim}_{Ω \to 0} H_{Ω}

Formulas (html):

Correct Categorie: hep-th

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/9705173

Formulas:

1-

w h e n

2-

L y m a n

3-

[F e / H]

4-

[F e / H]

5-

[F e / H]

6-

f_{λ} = f ([F e / H], T_{e f f}, \log g, R),

7-

F_{λ} = F_{λ}^{H} + F_{λ}^{H e} .

8-

\frac{d n_{i}}{d M_{i}} = α M_{i}^{- (x + 1)}

9-

F_{λ}^{H} = \sum_{i} n_{i} f_{λ, i}

10-

n_{i} = α \int_{M_{i} - δ M}^{M_{i} + δ M} M^{- (x + 1)} 𝑑 M .

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1111.4420

Formulas:

1-

0.1 - 0.25 M_{⊙}

2-

M \geq 0.03 M_{⊙}

3-

A_{V} \sim 1 mag

4-

C h a n d r a

5-

C h a n d r a

6-

M > 0.03 M_{⊙}

7-

3.6 \dots 8 μ

8-

α_{3 - 8 μ m}

9-

α_{3 - 8 μ m}

10-

- 0.5 \dots . - 1.8

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1905.01550

Formulas:

1-

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

2-

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

3-

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

4-

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

5-

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

6-

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

7-

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

8-

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

9-

σ = σ_{0} e x p {{(\frac{T_{0}}{T})}^{1 / (β + 1)}}

10-

β = 0, 1, 2, 3

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cs

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/9711213

Formulas:

1-

\frac{\partial^{2} 𝝃}{\partial t^{2}} = - \frac{1}{ρ} \nabla P^{'} + \frac{ρ^{'}}{ρ^{2}} \nabla P - \nabla Ψ_{T},

2-

ρ^{'} = - \nabla \cdot (ρ 𝝃),

3-

ρ T \partial (Δ S) / \partial t = - \nabla \cdot 𝐅^{'}

4-

(r, θ, φ)

5-

Ψ_{T} (r, θ, φ, t) = f r^{2} P_{n}^{| m |} (\cos θ) e^{i m (φ - ω t)}

6-

f = - G M_{p} / 4 D^{3},

7-

𝝃 = [ξ_{r} (r), ξ_{h} (r) \frac{\partial}{\partial θ}, ξ_{h} (r) \frac{\partial}{\sin θ \partial φ}] P_{n}^{| m |} (\cos θ) e^{i m (φ - ω t)} .

8-

\frac{d ξ_{r}}{d r}

9-

(- \frac{2}{r} + \bar{A} - \frac{d l n ρ}{d r}) ξ_{r} + [- \frac{m^{2} ω^{2} r ρ}{Γ_{1} P} + \frac{n (n + 1)}{r}] ξ_{h} + \frac{f r^{2} ρ}{Γ_{1} P},

10-

\frac{d ξ_{h}}{d r}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1011.4075

Formulas:

1-

M_{A B} \approx - 21

2-

ϕ (L) = ϕ_{*} {(L / L_{*})}^{α} \exp (- L / L_{*})

3-

M_{*} = - 2.5 \log_{10} (L_{*})

4-

m_{F 125 W} ≲ 27

5-

m_{F 606 W} = 26.9

6-

t_{e x p} = 2647

7-

m_{F 600 L P} = 26.4

8-

t_{e x p} = 2334

9-

m_{F 098 M} = 26.8

10-

t_{e x p} = 4515

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/0706.0088

Formulas:

1-

Δ f = ℓ (ℓ + 1) f

2-

S O (3)

3-

f (x_{1}, x_{2}, x_{3})

4-

f = (5 \cos^{3} θ - 3 \cos θ) / 2

5-

x_{3} = 0, x_{3} = \pm \sqrt{3 / 5}

6-

ϕ = (1 + \sqrt{5}) / 2

7-

(0, \pm ϕ, \pm 1)

8-

(\pm 1, 0, \pm ϕ)

9-

(\pm ϕ, \pm 1, 0)

10-

f = x_{1} x_{2} x_{3}

Formulas (html):

Correct Categorie: math

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/math/0611445

Formulas:

1-

\sum_{1 \leq i \leq h_{β}} {c_{β, i} (x) [\prod_{1 \leq j \leq k_{β, i}} D^{p_{β, i, j}} U_{α_{β, i, j}} (x)]} = f_{β} (x)

2-

x \in Ω \subseteq ℝ^{n}

3-

U = (U_{1}, \dots, U_{a}) : Ω ⟶ ℝ^{a}

4-

1 \leq α_{β, i, j} \leq a, 1 \leq β \leq b, p_{β, i, j} \in ℕ^{n}

5-

c_{β, i}, f_{β} \in 𝒞^{\infty} (Ω)

6-

T_{β} (x, D) U (x) = \sum_{1 \leq i \leq h_{β}} {c_{β, i} (x) [\prod_{1 \leq j \leq k_{β, i}} D^{p_{β, i, j}} U_{α_{β, i, j}} (x)]}

7-

\begin{matrix} T_{β} (x, D) U (x) = \\ = \sum_{1 \leq ρ \leq r_{β}} L_{β, ρ} (x, D) [U_{α_{β, ρ}} (x) P_{β, ρ} (x, D) U_{α_{β, ρ}} (x)] \end{matrix}

8-

L_{β, ρ} (x, D)

9-

P_{β, ρ} (x, D)

10-

U_{α_{β, ρ}} (x) P_{β, ρ} (x, D) U_{α_{β, ρ}} (x)

Formulas (html):

Correct Categorie: math

Guessed Categorie: hep-lat

Result: incorrect

Paper: https://arxiv.org/abs/hep-ph/9809499

Formulas:

1-

R = \frac{{(μ / e)}_{D A T A}}{{(μ / e)}_{M C}} = 0.61 \pm 0.03 \pm 0.05

2-

\sin^{2} (2 θ) = 1

3-

Δ m^{2} = 2.2 \times 10^{- 3}

4-

\bar{ν_{e}} \to \bar{ν_{x}}

5-

ν_{μ} \to ν_{e} X

6-

ν_{μ} \to ν_{s t e r i l e} X

7-

N = N_{0} e^{- \frac{m}{τ} \frac{L}{p}}

8-

\frac{L}{p} < 2.2 \times 10^{- 10}

9-

e^{- 1.4 \times 10^{- 11}}

10-

L = \cos^{2} a_{a b} (\bar{ν_{a}} ν_{a} + \bar{ν_{b}} ν_{b}) + \sin^{2} a_{a b} (\bar{ν_{a}} ν_{b} + \bar{ν_{a}} ν_{b})

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1101.4047

Formulas:

1-

p_{n} (K)

2-

p_{n} (K) / p_{n}

3-

p_{n} (K)

4-

p_{n} (K)

5-

p_{n} (K)

6-

C_{K} μ_{\emptyset}^{n} n^{α - 3 + N_{K}}, as n \to \infty,

7-

\frac{p_{n} (K) / p_{n}}{p_{n} (L) / p_{n}}

8-

\frac{p_{n} (K)}{p_{n} (L)} ≃ [\frac{C_{K}}{C_{L}}] .

9-

{lim}_{n \to \infty} p_{n}^{1 / n} = μ

10-

p_{n} (K)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: hep-lat

Result: incorrect

Paper: https://arxiv.org/abs/0711.2277

Formulas:

1-

{\frac{d N_{γ}}{d E_{γ}}}^{Band} (E_{γ}) = A_{γ} {\begin{matrix} {(\frac{E_{γ}}{100 k e V})}^{α_{γ}} e^{\frac{- E_{γ} (2 + α_{γ})}{E_{pk}}} & E_{γ} < ϵ_{γ}^{b} \\ {[\frac{(α_{γ} - β_{γ})}{2 + α_{γ}} \frac{E_{pk}}{100 k e V}]}^{α_{γ} - β_{γ}} e^{β_{γ} - α_{γ}} {(\frac{E_{γ}}{100 k e V})}^{β_{γ}} & E_{γ} > ϵ_{γ}^{b} \end{matrix} .

2-

ϵ_{γ}^{b} = \frac{α_{γ} - β_{γ}}{2 + α_{γ}} E_{pk} .

3-

p + γ \to Δ^{+} \to π^{+} [+ n] \to μ^{+} + ν_{μ} \to e^{+} + ν_{μ} + {\bar{ν}}_{μ} + ν_{e}

4-

p + γ \to Δ^{+} \to π^{0} + p .

5-

E_{p} \geq \frac{1}{{(1 + z)}^{2}} \frac{m_{Δ}^{2} - m_{p}^{2}}{4 E_{γ}} Γ^{2} .

6-

E_{ν} \geq \frac{1}{4} < x_{p \to π^{+}} > \frac{1}{{(1 + z)}^{2}} \frac{m_{Δ}^{2} - m_{p}^{2}}{4 E_{γ}} Γ^{2},

7-

< x_{p \to π^{+}} > \approx 1 / 5

8-

{\frac{d N_{γ}}{d E_{γ}}}^{A} = A_{γ} {\begin{matrix} {(\frac{E_{γ}}{100 k e V})}^{α_{γ}} & E_{γ} < ϵ_{γ}^{b} \\ {(\frac{E_{γ}}{100 k e V})}^{β_{γ}} & E_{γ} \geq ϵ_{γ}^{b} \end{matrix} .

9-

d N_{p} / d E_{p} \sim E_{p}^{- 2}

10-

{\frac{d N_{ν}}{d E_{ν}}}^{A} = A_{ν} {\begin{matrix} {(E / ϵ_{ν}^{b})}^{α_{ν}} & E < ϵ_{ν}^{b} \\ {(E / ϵ_{ν}^{b})}^{β_{ν}} & ϵ_{ν}^{b} \leq E \leq ϵ_{ν}^{s} \\ {(E / ϵ_{ν}^{b})}^{β_{ν}} {(E / ϵ_{ν}^{s})}^{- 2} & E > ϵ_{ν}^{s} \end{matrix},

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: gr-qc

Result: incorrect

Paper: https://arxiv.org/abs/1504.02221

Formulas:

1-

1108 < E_{γ} < 1300

2-

J^{P} = 3 / 2^{+}, 5 / 2^{+}

3-

ω \to π^{+} π^{-} π^{0}

4-

N (1680) 5 / 2^{+}

5-

N (1700) 3 / 2^{-}

6-

N (2190) 7 / 2^{-}

7-

ω \to π^{0} γ

8-

ω \to π^{0} γ

9-

\frac{d σ}{d Ω} = \frac{d σ_{0}}{d Ω} (1 - P_{γ}^{⊙} P_{T}^{z} E) .

10-

\cos θ_{C M S}^{ω}

Formulas (html):

Correct Categorie: nucl-ex

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/2011.05916

Formulas:

1-

V = K Δ μ

2-

K = 0.063 \pm 0.012 m / s

3-

K = 0.23 \pm 0.03 m / s

4-

30 - 100 c m / s^{2}

5-

\sim 60 m s

6-

Δ p (t)

7-

Δ p (t)

8-

Δ p_{0} = 0.16

9-

\frac{\partial {\vec{v}}_{n}}{\partial t} + ({\vec{v}}_{n} \nabla) {\vec{v}}_{n} = - \frac{1}{ρ_{n}} \nabla p_{n} + \frac{η_{n}}{ρ_{n}} △ {\vec{v}}_{n}

10-

t \to t \frac{R}{U}, r \to r R, v_{n} \to v_{n} U, p_{n} \to ρ_{n} U^{2} p_{n}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/0811.2165

Formulas:

1-

J_{z} = \pm 3 / 2

2-

S_{z} = - 5 / 2

3-

S_{z} = 5 / 2

4-

S_{z} = - 5 / 2

5-

τ_{X - M n}

6-

D_{0} S_{z}^{2}

7-

D_{0} = 7 μ

8-

ρ_{+ 5 / 2} (t)

9-

ρ_{+ 5 / 2} (0) = 1

10-

⟨ ρ_{+ 5 / 2} (t) ⟩

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: math

Result: incorrect

Run 10667649 (TestAgent)