Run 6831306

Paper: https://arxiv.org/abs/1504.06776

Formulas:

1-

{(1 - I)}^{2}

2-

G = p \cdot (1 - p)

3-

θ = a b s (G_{P} - (G_{s} + G_{b}))

4-

w = \frac{1 - ϵ}{ϵ}

5-

𝐱^{'} = S^{- 1} 𝐱

6-

u, g, r, i, z

7-

u, g, r, i, z

8-

E (m) = \frac{N_{g a l a x i e s}^{s e l e c t e d}}{N_{g a l a x i e s}^{t o t a l}} \times 100

9-

I (m) = \frac{N_{s t a r s}^{s e l e c t e d}}{N_{s t a r s + g a l a x i e s}^{s e l e c t e d}} \times 100

10-

N_{s t a r s}^{s e l e c t e d}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: cs

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0512423

Formulas:

1-

T = \exp (- τ_{M} - τ_{A})

2-

1 + c o s^{2} (θ)

3-

T_{A} = \exp (- \frac{τ_{A}}{\sin (θ)})

4-

N_{O B S} = N_{γ L} T_{M 1} T_{A 1} (S_{A} + S_{M}) T_{M 2} T_{A 2}

5-

N_{O B S}

6-

N_{M O L} = N_{γ_{L}} T_{M 1} S_{M} T_{M 2}

7-

\frac{N_{O B S}}{N_{M O L}} = T_{A 1} T_{A 2} (1 + \frac{S_{A}}{S_{M}})

8-

τ_{A} = \frac{- 1}{\frac{1}{s i n θ_{1}} + \frac{1}{s i n θ_{2}}} (\ln (\frac{N_{O B S}}{N_{M O L}}) - \ln (1 + \frac{S_{A}}{S_{M}}))

9-

τ_{A} = - \frac{s i n θ_{1} s i n θ_{2}}{s i n θ_{1} + s i n θ_{2}} \ln (\frac{N_{O B S}}{N_{M O L}})

10-

N_{M O L}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0207229

Formulas:

1-

P_{n} = λ_{n} t_{n}

2-

t = \sum_{n} t_{n}

3-

P (t) = Π_{n} λ_{n} t_{n} = Π_{n} λ_{n} \cdot Π_{n} t_{n} .

4-

t_{n} = t / N

5-

P_{m a x} (t) = {(\frac{t}{N})}^{N} \cdot Π_{n} λ_{n} .

6-

P_{1} = λ_{1} t_{1}

7-

t_{1} = t / N

8-

t_{1} = {0.1}_{- 0.1}^{+ 0.5} Gyr .

9-

t ≃ 4 G y r .

10-

W_{k} (t)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0310029

Formulas:

1-

\sim 10^{12} L_{⊙}

2-

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

3-

L_{IR} = 10^{11.8} L_{⊙}

4-

\sim {1.8}^{''} = 0.88 kpc

5-

\sim 1^{''} = 0.49 kpc

6-

\sim {0.05}^{''} = 25 pc

7-

E_{B - K} = {(B - K)}_{obs} - {(B - K)}_{intrinsic}

8-

A_{V} = 0.825 E_{B - K}

9-

V_{corr} = V - A_{V}

10-

A_{V} (N 1) = 2.35

Formulas (html):

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id="S2.SS3.p5.3.m3.2.2.2.3" xref="S2.SS3.p5.3.m3.2.2.2.3.cmml">-</mo><msub id="S2.SS3.p5.3.m3.2.2.2.2" xref="S2.SS3.p5.3.m3.2.2.2.2.cmml"><mrow id="S2.SS3.p5.3.m3.2.2.2.2.1.1" xref="S2.SS3.p5.3.m3.2.2.2.2.1.1.1.cmml"><mo stretchy="false" id="S2.SS3.p5.3.m3.2.2.2.2.1.1.2" xref="S2.SS3.p5.3.m3.2.2.2.2.1.1.1.cmml">(</mo><mrow id="S2.SS3.p5.3.m3.2.2.2.2.1.1.1" xref="S2.SS3.p5.3.m3.2.2.2.2.1.1.1.cmml"><mi id="S2.SS3.p5.3.m3.2.2.2.2.1.1.1.2" xref="S2.SS3.p5.3.m3.2.2.2.2.1.1.1.2.cmml">B</mi><mo id="S2.SS3.p5.3.m3.2.2.2.2.1.1.1.1" xref="S2.SS3.p5.3.m3.2.2.2.2.1.1.1.1.cmml">-</mo><mi id="S2.SS3.p5.3.m3.2.2.2.2.1.1.1.3" xref="S2.SS3.p5.3.m3.2.2.2.2.1.1.1.3.cmml">K</mi></mrow><mo stretchy="false" id="S2.SS3.p5.3.m3.2.2.2.2.1.1.3" xref="S2.SS3.p5.3.m3.2.2.2.2.1.1.1.cmml">)</mo></mrow><mi id="S2.SS3.p5.3.m3.2.2.2.2.3" xref="S2.SS3.p5.3.m3.2.2.2.2.3.cmml">intrinsic</mi></msub></mrow></mrow></math>, <math><mrow id="S2.SS3.p5.4.m4.1.1" xref="S2.SS3.p5.4.m4.1.1.cmml"><msub id="S2.SS3.p5.4.m4.1.1.2" xref="S2.SS3.p5.4.m4.1.1.2.cmml"><mi id="S2.SS3.p5.4.m4.1.1.2.2" xref="S2.SS3.p5.4.m4.1.1.2.2.cmml">A</mi><mi id="S2.SS3.p5.4.m4.1.1.2.3" xref="S2.SS3.p5.4.m4.1.1.2.3.cmml">V</mi></msub><mo id="S2.SS3.p5.4.m4.1.1.1" xref="S2.SS3.p5.4.m4.1.1.1.cmml">=</mo><mrow id="S2.SS3.p5.4.m4.1.1.3" xref="S2.SS3.p5.4.m4.1.1.3.cmml"><mn id="S2.SS3.p5.4.m4.1.1.3.2" xref="S2.SS3.p5.4.m4.1.1.3.2.cmml">0.825</mn><mo id="S2.SS3.p5.4.m4.1.1.3.1" xref="S2.SS3.p5.4.m4.1.1.3.1.cmml">⁢</mo><msub id="S2.SS3.p5.4.m4.1.1.3.3" xref="S2.SS3.p5.4.m4.1.1.3.3.cmml"><mi id="S2.SS3.p5.4.m4.1.1.3.3.2" xref="S2.SS3.p5.4.m4.1.1.3.3.2.cmml">E</mi><mrow id="S2.SS3.p5.4.m4.1.1.3.3.3" xref="S2.SS3.p5.4.m4.1.1.3.3.3.cmml"><mi id="S2.SS3.p5.4.m4.1.1.3.3.3.2" xref="S2.SS3.p5.4.m4.1.1.3.3.3.2.cmml">B</mi><mo id="S2.SS3.p5.4.m4.1.1.3.3.3.1" xref="S2.SS3.p5.4.m4.1.1.3.3.3.1.cmml">-</mo><mi id="S2.SS3.p5.4.m4.1.1.3.3.3.3" xref="S2.SS3.p5.4.m4.1.1.3.3.3.3.cmml">K</mi></mrow></msub></mrow></mrow></math>, <math><mrow id="S2.SS3.p5.21.m21.1.1" xref="S2.SS3.p5.21.m21.1.1.cmml"><msub id="S2.SS3.p5.21.m21.1.1.2" xref="S2.SS3.p5.21.m21.1.1.2.cmml"><mi id="S2.SS3.p5.21.m21.1.1.2.2" xref="S2.SS3.p5.21.m21.1.1.2.2.cmml">V</mi><mi id="S2.SS3.p5.21.m21.1.1.2.3" xref="S2.SS3.p5.21.m21.1.1.2.3.cmml">corr</mi></msub><mo id="S2.SS3.p5.21.m21.1.1.1" xref="S2.SS3.p5.21.m21.1.1.1.cmml">=</mo><mrow id="S2.SS3.p5.21.m21.1.1.3" xref="S2.SS3.p5.21.m21.1.1.3.cmml"><mi id="S2.SS3.p5.21.m21.1.1.3.2" xref="S2.SS3.p5.21.m21.1.1.3.2.cmml">V</mi><mo id="S2.SS3.p5.21.m21.1.1.3.1" xref="S2.SS3.p5.21.m21.1.1.3.1.cmml">-</mo><msub id="S2.SS3.p5.21.m21.1.1.3.3" xref="S2.SS3.p5.21.m21.1.1.3.3.cmml"><mi id="S2.SS3.p5.21.m21.1.1.3.3.2" xref="S2.SS3.p5.21.m21.1.1.3.3.2.cmml">A</mi><mi id="S2.SS3.p5.21.m21.1.1.3.3.3" xref="S2.SS3.p5.21.m21.1.1.3.3.3.cmml">V</mi></msub></mrow></mrow></math>, <math><mrow id="S2.SS3.p6.3.m3.1.1" xref="S2.SS3.p6.3.m3.1.1.cmml"><mrow id="S2.SS3.p6.3.m3.1.1.1" xref="S2.SS3.p6.3.m3.1.1.1.cmml"><msub id="S2.SS3.p6.3.m3.1.1.1.3" xref="S2.SS3.p6.3.m3.1.1.1.3.cmml"><mi id="S2.SS3.p6.3.m3.1.1.1.3.2" xref="S2.SS3.p6.3.m3.1.1.1.3.2.cmml">A</mi><mi id="S2.SS3.p6.3.m3.1.1.1.3.3" xref="S2.SS3.p6.3.m3.1.1.1.3.3.cmml">V</mi></msub><mo id="S2.SS3.p6.3.m3.1.1.1.2" xref="S2.SS3.p6.3.m3.1.1.1.2.cmml">⁢</mo><mrow id="S2.SS3.p6.3.m3.1.1.1.1.1" xref="S2.SS3.p6.3.m3.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S2.SS3.p6.3.m3.1.1.1.1.1.2" xref="S2.SS3.p6.3.m3.1.1.1.1.1.1.cmml">(</mo><mrow id="S2.SS3.p6.3.m3.1.1.1.1.1.1" xref="S2.SS3.p6.3.m3.1.1.1.1.1.1.cmml"><mi id="S2.SS3.p6.3.m3.1.1.1.1.1.1.2" xref="S2.SS3.p6.3.m3.1.1.1.1.1.1.2.cmml">N</mi><mo id="S2.SS3.p6.3.m3.1.1.1.1.1.1.1" xref="S2.SS3.p6.3.m3.1.1.1.1.1.1.1.cmml">⁢</mo><mn id="S2.SS3.p6.3.m3.1.1.1.1.1.1.3" xref="S2.SS3.p6.3.m3.1.1.1.1.1.1.3.cmml">1</mn></mrow><mo stretchy="false" id="S2.SS3.p6.3.m3.1.1.1.1.1.3" xref="S2.SS3.p6.3.m3.1.1.1.1.1.1.cmml">)</mo></mrow></mrow><mo id="S2.SS3.p6.3.m3.1.1.2" xref="S2.SS3.p6.3.m3.1.1.2.cmml">=</mo><mn id="S2.SS3.p6.3.m3.1.1.3" xref="S2.SS3.p6.3.m3.1.1.3.cmml">2.35</mn></mrow></math>

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0504456

Formulas:

1-

27 h^{- 3} {Gpc}^{3}

2-

2.2 \times 10^{12} h^{- 1} M_{⊙}

3-

k > 0.15 h {Mpc}^{- 1}

4-

k \sim < 0.07 h {Mpc}^{- 1}

5-

300 km s^{- 1}

6-

M > 1.8 \times 10^{14} h^{- 1} M_{⊙}

7-

r^{2} ξ (r)

8-

P / P_{ref} = A + B k

9-

\frac{σ}{P} = 2 π \sqrt{\frac{1}{V k^{2} Δ k}} (\frac{1 + \bar{n} P}{\bar{n} P}),

10-

σ_{V} = 300 k m s^{- 1}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0606101

Formulas:

1-

- \frac{G M_{d}}{\sqrt{R^{2} + {(a + \sqrt{z^{2} + b^{2}})}^{2}}}; Φ_{b} = - \frac{G M_{b}}{r + c};

2-

- \frac{G M_{h} \ln (1 + r / r_{s})}{r} {[\ln (1 + c_{200}) - \frac{c_{200}}{1 + c_{200}}]}^{- 1} .

3-

M_{d} = 8.4 \times 10^{10} M_{⊙}

4-

M_{b} = 3.3 \times 10^{10} M_{⊙}

5-

M_{h} (r_{200}) = 6.8 \times 10^{11} M_{⊙}

6-

c_{200} = r_{200} / r_{s} = 22

7-

c = r_{vir} / r_{s} = 20

8-

ϵ = Ψ - v^{2} / 2

9-

Ψ = - Φ_{N F W} + Φ_{N F W} (\infty)

10-

f_{⋆} (ϵ) / f_{N F W} (ϵ) \times N (ϵ)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1407.7522

Formulas:

1-

ν_{α} (i, 𝐤) = \frac{1}{ℏ} \frac{\partial ϵ (i, 𝐤)}{\partial 𝐤_{α}}

2-

ϵ (i, 𝐤)

3-

ν_{α} (i, 𝐤)

4-

S_{α β} (T, μ) = \frac{1}{e T} \frac{\int ν_{α} (i, 𝐤) ν_{β} (i, 𝐤) (ϵ - μ) [- \frac{\partial f_{μ} (T, ϵ)}{\partial ϵ}] 𝑑 ϵ}{\int ν_{α} (i, 𝐤) ν_{β} (i, 𝐤) [- \frac{\partial f_{μ} (T, ϵ)}{\partial ϵ}] 𝑑 ϵ}

5-

\frac{σ_{α β} (T, μ)}{τ (i, 𝐤)} = \frac{1}{V} \int e {}^{2}ν_{α} (i, 𝐤) ν_{β} (i, 𝐤) [- \frac{\partial f_{μ} (T, ϵ)}{\partial ϵ}] 𝑑 ϵ

6-

S^{2} σ / τ

7-

S_{a v} = (S_{x x} + S_{y y} + S_{z z}) / 3

8-

S^{2} σ / τ

9-

Z T = S^{2} σ / κ_{t o t a l}

10-

κ_{t o t a l}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/cond-mat/9508060

Formulas:

1-

λ = (e^{2} / ϵ l_{0}) / ℏ ω_{c}

2-

ℏ ω_{c} = ℏ e B / m^{*} c

3-

e^{2} / ϵ l_{0}

4-

l_{0} = \sqrt{ℏ c / e B}

5-

λ = (e^{2} / ϵ l_{0}) / ℏ ω_{c}

6-

Δ_{h} ≃ 0.023 e^{2} / ϵ l_{0}

7-

Δ_{e} ≃ 0.05 e^{2} / ϵ l_{0}

8-

B = S {(l_{0} / R)}^{2}

9-

𝐀 = 𝐞_{ϕ} (ℏ S / e R) \cot θ

10-

2 S = q (N - 1)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1407.7387

Formulas:

1-

u (x, n)

2-

G^{h} (z)

3-

\frac{d n}{d y} = \frac{x_{E}}{σ_{i n e l}} \cdot \frac{d σ}{d x_{F}} = \sum_{n = 1}^{\infty} w_{n} \cdot ϕ_{n}^{h} (x) + w_{D} \cdot ϕ_{D}^{h} (x),

4-

ϕ_{n}^{h} (x)

5-

w_{D} \cdot ϕ_{D}^{h} (x)

6-

ϕ_{n}^{h} (x)

7-

f_{q q}^{h} (x_{+}, n) \cdot f_{q}^{h} (x_{-}, n) + f_{q}^{h} (x_{+}, n) \cdot f_{q q}^{h} (x_{-}, n)

8-

2 (n - 1) \cdot f_{s}^{h} (x_{+}, n) \cdot f_{s}^{h} (x_{-}, n),

9-

\frac{1}{2} [\sqrt{4 m_{T}^{2} / s + x^{2}} \pm x],

10-

f_{q q}^{h} (x_{+}, n)

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/9806291

Formulas:

1-

θ^{2} = \frac{1}{D^{2}} \int_{0}^{D} z^{2} ψ (z) d z

2-

θ_{H}^{2} = (4 \ln 2) θ^{2}

3-

τ_{sc} = \frac{1}{2 c D} \int_{0}^{D} z (D - z) ψ (z) d z

4-

2 π τ_{sc} Δ ν = 1

5-

4 \ln 2 \frac{D ψ_{0}}{3} [1 + 3 {(1 - x)}^{2} \frac{ψ_{1}}{D ψ_{0}}]

6-

\frac{D}{4 c} \frac{D ψ_{0}}{3} [1 + 6 x (1 - x) \frac{ψ_{1}}{D ψ_{0}}]

7-

θ_{τ}^{2} = 4 \ln 2 (\frac{4 c τ_{sc}}{D})

8-

θ_{τ}^{2} = 4 \ln 2 \frac{D ψ_{0}}{3} [1 + 6 x (1 - x) \frac{ψ_{1}}{D ψ_{0}}]

9-

ψ_{1} / D ψ_{0}

10-

Y = (ψ_{1} / D ψ_{0})

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1006.2994

Formulas:

1-

(x, y, z, t)

2-

(x^{'}, y^{'}, z^{'}, t^{'})

3-

x = y = z = t = 0 ⟹ x^{'} = y^{'} = z^{'} = t^{'} = 0

4-

t = t^{'} = 0

5-

\begin{matrix} x^{'} = X (x, y, z, t, v) \\ y^{'} = Y (x, y, z, t, v) \\ z^{'} = Z (x, y, z, t, v) \\ t^{'} = T (x, y, z, t, v) \end{matrix}

6-

f_{v} : ℝ^{4} ⟶ ℝ^{4}

7-

x, y, z, t \in ℝ

8-

\begin{matrix} f_{v} (x, y, z, t) = \\ = (X (x, y, z, t, v), Y (x, y, z, t, v), Z (x, y, z, t, v), T (x, y, z, t, v)) \end{matrix}

9-

u^{'} = f_{v} (u), u, u^{'} \in ℝ^{4}, v \in ℝ

10-

\begin{matrix} \forall v \in ℝ : \\ \exists M > 0 : \\ \forall u \in ℝ^{4} : \\ || u || \leq 1 ⟹ || f_{v} (u) || \leq M \end{matrix}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/1702.03524

Formulas:

1-

D^{'} (G)

2-

D^{'} (G) \leq ⌈ \sqrt{Δ (G)} ⌉ + 1

3-

D^{'} (G) \leq ⌈ \sqrt{Δ} ⌉

4-

G = (V, E)

5-

N_{G} (v) = {u \in V (G) : u v \in E (G)}

6-

\deg_{G} (v)

7-

\deg_{G} (v)

8-

\deg_{G} (v) = k

9-

D^{'} (G)

10-

D^{'} (P_{n}) = 2

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/gr-qc/0410051

Formulas:

1-

n (n - 1) / 2

2-

S_{12} \equiv \int_{- T / 2}^{T / 2} 𝑑 t \int_{- T / 2}^{T / 2} 𝑑 t^{'} S_{1} (t) S_{2} (t^{'}) Q (t - t^{'}) = \int_{- \infty}^{\infty} 𝑑 f {\tilde{S}}_{1}^{*} (f) {\tilde{S}}_{2} (f) \tilde{Q} (f),

3-

{\tilde{S}}_{1} (f)

4-

{\tilde{S}}_{2} (f^{'})

5-

| f - f^{'} | < 1 / T

6-

S_{1, 2} = s_{1, 2} + N_{1, 2}

7-

{[SNR (2 | 2)]}^{2} \equiv \frac{⟨ S_{12} ⟩}{σ_{12}} = \frac{⟨ S_{12} ⟩}{{(⟨ S_{12}^{2} ⟩ - {⟨ S_{12} ⟩}^{2})}^{1 / 2}} = \frac{⟨ s_{1} s_{2} ⟩}{{⟨ N_{1}^{2} N_{2}^{2} ⟩}^{1 / 2}},

8-

s_{i} (t_{i}, x_{i}) = \int_{- \infty}^{\infty} 𝑑 f_{i} \int 𝑑 Ω_{i} {\tilde{h}}_{A} (f_{i}, Ω_{i}) e^{2 π i f_{i} (t_{i} - Ω_{i} x_{i})} F^{A} (Ω_{i}),

9-

⟨ \tilde{h} (f_{1}, Ω_{1}) \tilde{h} (f_{2}, Ω_{2}) ⟩ = δ (f_{1} + f_{2}) \frac{1}{4 π} δ^{2} (Ω_{1}, Ω_{2}) \frac{1}{2} S_{h} (f_{1}),

10-

⟨ N_{i} (f_{1}) N_{j} (f_{2}) ⟩ = δ_{i j} δ (f_{1} + f_{2}) \frac{1}{2} S_{N, i} (f_{1}) .

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: hep-th

Result: incorrect

Paper: https://arxiv.org/abs/2003.09966

Formulas:

1-

P^{4 +} + P^{4 +} \leftrightarrow P^{3 +} + P^{5 +}

2-

x > x_{LP} \approx 0.28

3-

ε^{'} (T)

4-

ε^{''} (T)

5-

ε^{'} (T)

6-

ε^{'} (T)

7-

ε^{''} (T)

8-

ε {(T)}^{- 1} \sim T^{2}

9-

ε^{'} (T) \sim {(T - T_{C})}^{- 2}

10-

1 / ε (T) \sim T

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1802.02441

Formulas:

1-

A^{↑} + B \to C + X

2-

A_{N} = \frac{d σ^{↑} - d σ^{↓}}{d σ^{↑} + d σ^{↓}}

3-

γ g \to c \bar{c}

4-

d σ^{↑} - d σ^{↓} = F_{J / ψ} \int_{4 m_{c}^{2}}^{4 m_{D}^{2}} 𝑑 M^{2} \int d^{2} 𝐤_{⟂ g} Δ^{N} f_{g / p^{↑}} (x_{g}, 𝐤_{⟂ g}) f_{γ / e} (x_{γ}, 𝐤_{⟂ γ}) {\hat{σ}}_{0}

5-

d σ^{↑} + d σ^{↓} = 2 F_{J / ψ} \int_{4 m_{c}^{2}}^{4 m_{D}^{2}} 𝑑 M^{2} \int d^{2} 𝐤_{⟂ g} f_{g / p^{↑}} (x_{g}, 𝐤_{⟂ g}) f_{γ / e} (x_{γ}, 𝐤_{⟂ γ}) {\hat{σ}}_{0}

6-

d σ^{↑ (↓)} = \frac{d σ^{↑ (↓)}}{d y d^{2} 𝐪_{T}}

7-

𝐤_{⟂ γ} = 𝐪_{T} - 𝐤_{⟂ g}

8-

{\hat{σ}}_{0} (M^{2})

9-

γ g \to c \bar{c}

10-

f_{g / p} (x, k_{⟂}; Q) = f_{g / p} (x, Q) \frac{1}{π ⟨ k_{⟂}^{2} ⟩} e^{- k_{⟂}^{2} / ⟨ k_{⟂}^{2} ⟩} .

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: nucl-ex

Result: incorrect

Paper: https://arxiv.org/abs/math/9909133

Formulas:

1-

ψ \in L^{2} (ℝ)

2-

{D^{n} T^{l} : n, l \in ℤ}

3-

{D^{n} T^{l} ψ : n, l \in ℤ}

4-

L^{2} (ℝ)

5-

L^{2} (ℝ)

6-

D f (x) = \sqrt{2} f (2 x)

7-

T f (x) = f (x - 1)

8-

V_{j} = \bar{s p a n} {D^{n} T^{l} ψ : n < j, l \in ℤ}

9-

V_{j} \subset V_{j + 1}

10-

D V_{j} = V_{j + 1}

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/1410.5556

Formulas:

1-

B (E 2)

2-

π [422] 5 / 2^{+}

3-

ν [532] 5 / 2^{-}

4-

\begin{matrix} h^{'} & = h - ω_{rot} J_{x} \\ = \sum_{μ} e_{μ}^{'} a_{μ}^{†} a_{μ} + \sum_{\bar{μ}} e_{\bar{μ}}^{'} a_{\bar{μ}}^{†} a_{\bar{μ}} + const, \end{matrix}

5-

\begin{matrix} H_{int} & = - \sum_{τ = 1, 2} G_{τ} {\tilde{P}}_{τ}^{†} {\tilde{P}}_{τ} - \frac{1}{2} \sum_{K = 0, 1, 2} κ_{K}^{(+)} Q_{K}^{'', (+), †} Q_{K}^{'', (+)} - \frac{1}{2} \sum_{K = 1, 2} κ_{K}^{(-)} Q_{K}^{'', (-), †} Q_{K}^{'', (-)} \\ = \sum_{n} ω_{n} X_{n}^{†} X_{n} . \end{matrix}

6-

r = \exp (- i π α) = 1

7-

\begin{matrix} H_{couple} (γ) & = \sum_{μ ν} Λ_{γ} (μ ν) (X_{γ}^{†} a_{μ}^{†} a_{ν} + X_{γ} a_{ν}^{†} a_{μ}) \\ + \sum_{μ \bar{ν}} Λ_{\bar{γ}} (μ \bar{ν}) (X_{\bar{γ}}^{†} a_{μ}^{†} a_{\bar{ν}} + X_{\bar{γ}} a_{\bar{ν}}^{†} a_{μ}) \\ + sig. conj. \end{matrix}

8-

1 q p \otimes {(γ or \bar{γ})}^{n}

9-

{(1 q p)}_{r = \pm i} \otimes γ

10-

{(1 q p)}_{r = \mp i} \otimes \bar{γ}

Formulas (html):

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xref="S2.E2.m1.12.12.12.12.10.10.cmml"><mi id="S2.E2.m1.12.12.12.12.10.10.2" xref="S2.E2.m1.12.12.12.12.10.10.2.cmml">P</mi><mo stretchy="false" id="S2.E2.m1.12.12.12.12.10.10.1" xref="S2.E2.m1.12.12.12.12.10.10.1.cmml">~</mo></mover><mi id="S2.E2.m1.13.13.13.13.11.11.1" xref="S2.E2.m1.13.13.13.13.11.11.1.cmml">τ</mi></msub></mrow></mrow></mrow><mo id="S2.E2.m1.14.14.14.14.12.12" xref="S2.E2.m1.14.14.14.14.12.12.cmml">-</mo><mrow id="S2.E2.m1.39.39.39.39.37.39.2"><mfrac id="S2.E2.m1.15.15.15.15.13.13" xref="S2.E2.m1.15.15.15.15.13.13.cmml"><mn id="S2.E2.m1.15.15.15.15.13.13.2" xref="S2.E2.m1.15.15.15.15.13.13.2.cmml">1</mn><mn id="S2.E2.m1.15.15.15.15.13.13.3" xref="S2.E2.m1.15.15.15.15.13.13.3.cmml">2</mn></mfrac><mo id="S2.E2.m1.39.39.39.39.37.39.2.1" xref="S2.E2.m1.51.51.1.1.1.cmml">⁢</mo><mrow id="S2.E2.m1.39.39.39.39.37.39.2.2"><munder id="S2.E2.m1.39.39.39.39.37.39.2.2.1"><mo largeop="true" movablelimits="false" symmetric="true" id="S2.E2.m1.16.16.16.16.14.14" xref="S2.E2.m1.16.16.16.16.14.14.cmml">∑</mo><mrow id="S2.E2.m1.17.17.17.17.15.15.1" xref="S2.E2.m1.17.17.17.17.15.15.1.cmml"><mi id="S2.E2.m1.17.17.17.17.15.15.1.5" xref="S2.E2.m1.17.17.17.17.15.15.1.5.cmml">K</mi><mo id="S2.E2.m1.17.17.17.17.15.15.1.4" xref="S2.E2.m1.17.17.17.17.15.15.1.4.cmml">=</mo><mrow id="S2.E2.m1.17.17.17.17.15.15.1.6.2" xref="S2.E2.m1.17.17.17.17.15.15.1.6.1.cmml"><mn id="S2.E2.m1.17.17.17.17.15.15.1.1" xref="S2.E2.m1.17.17.17.17.15.15.1.1.cmml">0</mn><mo id="S2.E2.m1.17.17.17.17.15.15.1.6.2.1" xref="S2.E2.m1.17.17.17.17.15.15.1.6.1.cmml">,</mo><mn id="S2.E2.m1.17.17.17.17.15.15.1.2" xref="S2.E2.m1.17.17.17.17.15.15.1.2.cmml">1</mn><mo id="S2.E2.m1.17.17.17.17.15.15.1.6.2.2" xref="S2.E2.m1.17.17.17.17.15.15.1.6.1.cmml">,</mo><mn id="S2.E2.m1.17.17.17.17.15.15.1.3" xref="S2.E2.m1.17.17.17.17.15.15.1.3.cmml">2</mn></mrow></mrow></munder><mrow id="S2.E2.m1.39.39.39.39.37.39.2.2.2"><msubsup id="S2.E2.m1.39.39.39.39.37.39.2.2.2.2"><mi id="S2.E2.m1.18.18.18.18.16.16" xref="S2.E2.m1.18.18.18.18.16.16.cmml">κ</mi><mi id="S2.E2.m1.19.19.19.19.17.17.1" xref="S2.E2.m1.19.19.19.19.17.17.1.cmml">K</mi><mrow id="S2.E2.m1.20.20.20.20.18.18.1.3"><mo stretchy="false" id="S2.E2.m1.20.20.20.20.18.18.1.3.1">(</mo><mo id="S2.E2.m1.20.20.20.20.18.18.1.1" xref="S2.E2.m1.20.20.20.20.18.18.1.1.cmml">+</mo><mo stretchy="false" id="S2.E2.m1.20.20.20.20.18.18.1.3.2">)</mo></mrow></msubsup><mo id="S2.E2.m1.39.39.39.39.37.39.2.2.2.1" xref="S2.E2.m1.51.51.1.1.1.cmml">⁢</mo><msubsup id="S2.E2.m1.39.39.39.39.37.39.2.2.2.3"><mi id="S2.E2.m1.21.21.21.21.19.19" xref="S2.E2.m1.21.21.21.21.19.19.cmml">Q</mi><mi id="S2.E2.m1.22.22.22.22.20.20.1" xref="S2.E2.m1.22.22.22.22.20.20.1.cmml">K</mi><mrow id="S2.E2.m1.23.23.23.23.21.21.1.4" xref="S2.E2.m1.23.23.23.23.21.21.1.5.cmml"><mo mathsize="142%" stretchy="false" id="S2.E2.m1.23.23.23.23.21.21.1.3.1" xref="S2.E2.m1.23.23.23.23.21.21.1.3.1.cmml">′′</mo><mo id="S2.E2.m1.23.23.23.23.21.21.1.4.3" xref="S2.E2.m1.23.23.23.23.21.21.1.5.cmml">⁣</mo><mrow id="S2.E2.m1.23.23.23.23.21.21.1.4.2.2" xref="S2.E2.m1.23.23.23.23.21.21.1.5.cmml"><mo stretchy="false" id="S2.E2.m1.23.23.23.23.21.21.1.4.2.2.1" xref="S2.E2.m1.23.23.23.23.21.21.1.5.cmml">(</mo><mo id="S2.E2.m1.23.23.23.23.21.21.1.1" xref="S2.E2.m1.23.23.23.23.21.21.1.1.cmml">+</mo><mo stretchy="false" id="S2.E2.m1.23.23.23.23.21.21.1.4.2.2.2" xref="S2.E2.m1.23.23.23.23.21.21.1.5.cmml">)</mo></mrow><mo id="S2.E2.m1.23.23.23.23.21.21.1.4.4" xref="S2.E2.m1.23.23.23.23.21.21.1.5.cmml">⁣</mo><mo id="S2.E2.m1.23.23.23.23.21.21.1.2" xref="S2.E2.m1.23.23.23.23.21.21.1.2.cmml">†</mo></mrow></msubsup><mo id="S2.E2.m1.39.39.39.39.37.39.2.2.2.1a" xref="S2.E2.m1.51.51.1.1.1.cmml">⁢</mo><msubsup id="S2.E2.m1.39.39.39.39.37.39.2.2.2.4"><mi id="S2.E2.m1.24.24.24.24.22.22" xref="S2.E2.m1.24.24.24.24.22.22.cmml">Q</mi><mi id="S2.E2.m1.25.25.25.25.23.23.1" xref="S2.E2.m1.25.25.25.25.23.23.1.cmml">K</mi><mrow id="S2.E2.m1.26.26.26.26.24.24.1.3" xref="S2.E2.m1.26.26.26.26.24.24.1.4.cmml"><mo mathsize="142%" stretchy="false" id="S2.E2.m1.26.26.26.26.24.24.1.2.1" xref="S2.E2.m1.26.26.26.26.24.24.1.2.1.cmml">′′</mo><mo id="S2.E2.m1.26.26.26.26.24.24.1.3.3" xref="S2.E2.m1.26.26.26.26.24.24.1.4.cmml">⁣</mo><mrow id="S2.E2.m1.26.26.26.26.24.24.1.3.2.2" xref="S2.E2.m1.26.26.26.26.24.24.1.4.cmml"><mo stretchy="false" id="S2.E2.m1.26.26.26.26.24.24.1.3.2.2.1" xref="S2.E2.m1.26.26.26.26.24.24.1.4.cmml">(</mo><mo id="S2.E2.m1.26.26.26.26.24.24.1.1" xref="S2.E2.m1.26.26.26.26.24.24.1.1.cmml">+</mo><mo stretchy="false" id="S2.E2.m1.26.26.26.26.24.24.1.3.2.2.2" xref="S2.E2.m1.26.26.26.26.24.24.1.4.cmml">)</mo></mrow></mrow></msubsup></mrow></mrow></mrow><mo id="S2.E2.m1.14.14.14.14.12.12a" xref="S2.E2.m1.14.14.14.14.12.12.cmml">-</mo><mrow id="S2.E2.m1.39.39.39.39.37.39.3"><mfrac id="S2.E2.m1.28.28.28.28.26.26" xref="S2.E2.m1.28.28.28.28.26.26.cmml"><mn id="S2.E2.m1.28.28.28.28.26.26.2" xref="S2.E2.m1.28.28.28.28.26.26.2.cmml">1</mn><mn id="S2.E2.m1.28.28.28.28.26.26.3" xref="S2.E2.m1.28.28.28.28.26.26.3.cmml">2</mn></mfrac><mo id="S2.E2.m1.39.39.39.39.37.39.3.1" xref="S2.E2.m1.51.51.1.1.1.cmml">⁢</mo><mrow id="S2.E2.m1.39.39.39.39.37.39.3.2"><munder id="S2.E2.m1.39.39.39.39.37.39.3.2.1"><mo largeop="true" movablelimits="false" symmetric="true" id="S2.E2.m1.29.29.29.29.27.27" xref="S2.E2.m1.29.29.29.29.27.27.cmml">∑</mo><mrow id="S2.E2.m1.30.30.30.30.28.28.1" xref="S2.E2.m1.30.30.30.30.28.28.1.cmml"><mi id="S2.E2.m1.30.30.30.30.28.28.1.4" xref="S2.E2.m1.30.30.30.30.28.28.1.4.cmml">K</mi><mo id="S2.E2.m1.30.30.30.30.28.28.1.3" xref="S2.E2.m1.30.30.30.30.28.28.1.3.cmml">=</mo><mrow id="S2.E2.m1.30.30.30.30.28.28.1.5.2" xref="S2.E2.m1.30.30.30.30.28.28.1.5.1.cmml"><mn id="S2.E2.m1.30.30.30.30.28.28.1.1" xref="S2.E2.m1.30.30.30.30.28.28.1.1.cmml">1</mn><mo id="S2.E2.m1.30.30.30.30.28.28.1.5.2.1" xref="S2.E2.m1.30.30.30.30.28.28.1.5.1.cmml">,</mo><mn id="S2.E2.m1.30.30.30.30.28.28.1.2" xref="S2.E2.m1.30.30.30.30.28.28.1.2.cmml">2</mn></mrow></mrow></munder><mrow id="S2.E2.m1.39.39.39.39.37.39.3.2.2"><msubsup id="S2.E2.m1.39.39.39.39.37.39.3.2.2.2"><mi id="S2.E2.m1.31.31.31.31.29.29" xref="S2.E2.m1.31.31.31.31.29.29.cmml">κ</mi><mi id="S2.E2.m1.32.32.32.32.30.30.1" xref="S2.E2.m1.32.32.32.32.30.30.1.cmml">K</mi><mrow id="S2.E2.m1.33.33.33.33.31.31.1.3"><mo stretchy="false" id="S2.E2.m1.33.33.33.33.31.31.1.3.1">(</mo><mo id="S2.E2.m1.33.33.33.33.31.31.1.1" xref="S2.E2.m1.33.33.33.33.31.31.1.1.cmml">-</mo><mo stretchy="false" id="S2.E2.m1.33.33.33.33.31.31.1.3.2">)</mo></mrow></msubsup><mo id="S2.E2.m1.39.39.39.39.37.39.3.2.2.1" xref="S2.E2.m1.51.51.1.1.1.cmml">⁢</mo><msubsup id="S2.E2.m1.39.39.39.39.37.39.3.2.2.3"><mi id="S2.E2.m1.34.34.34.34.32.32" xref="S2.E2.m1.34.34.34.34.32.32.cmml">Q</mi><mi id="S2.E2.m1.35.35.35.35.33.33.1" xref="S2.E2.m1.35.35.35.35.33.33.1.cmml">K</mi><mrow id="S2.E2.m1.36.36.36.36.34.34.1.4" xref="S2.E2.m1.36.36.36.36.34.34.1.5.cmml"><mo mathsize="142%" stretchy="false" id="S2.E2.m1.36.36.36.36.34.34.1.3.1" xref="S2.E2.m1.36.36.36.36.34.34.1.3.1.cmml">′′</mo><mo id="S2.E2.m1.36.36.36.36.34.34.1.4.3" xref="S2.E2.m1.36.36.36.36.34.34.1.5.cmml">⁣</mo><mrow id="S2.E2.m1.36.36.36.36.34.34.1.4.2.2" xref="S2.E2.m1.36.36.36.36.34.34.1.5.cmml"><mo stretchy="false" id="S2.E2.m1.36.36.36.36.34.34.1.4.2.2.1" xref="S2.E2.m1.36.36.36.36.34.34.1.5.cmml">(</mo><mo id="S2.E2.m1.36.36.36.36.34.34.1.1" xref="S2.E2.m1.36.36.36.36.34.34.1.1.cmml">-</mo><mo stretchy="false" id="S2.E2.m1.36.36.36.36.34.34.1.4.2.2.2" xref="S2.E2.m1.36.36.36.36.34.34.1.5.cmml">)</mo></mrow><mo id="S2.E2.m1.36.36.36.36.34.34.1.4.4" xref="S2.E2.m1.36.36.36.36.34.34.1.5.cmml">⁣</mo><mo id="S2.E2.m1.36.36.36.36.34.34.1.2" xref="S2.E2.m1.36.36.36.36.34.34.1.2.cmml">†</mo></mrow></msubsup><mo id="S2.E2.m1.39.39.39.39.37.39.3.2.2.1a" xref="S2.E2.m1.51.51.1.1.1.cmml">⁢</mo><msubsup id="S2.E2.m1.39.39.39.39.37.39.3.2.2.4"><mi id="S2.E2.m1.37.37.37.37.35.35" xref="S2.E2.m1.37.37.37.37.35.35.cmml">Q</mi><mi id="S2.E2.m1.38.38.38.38.36.36.1" xref="S2.E2.m1.38.38.38.38.36.36.1.cmml">K</mi><mrow id="S2.E2.m1.39.39.39.39.37.37.1.3" xref="S2.E2.m1.39.39.39.39.37.37.1.4.cmml"><mo mathsize="142%" stretchy="false" id="S2.E2.m1.39.39.39.39.37.37.1.2.1" xref="S2.E2.m1.39.39.39.39.37.37.1.2.1.cmml">′′</mo><mo id="S2.E2.m1.39.39.39.39.37.37.1.3.3" xref="S2.E2.m1.39.39.39.39.37.37.1.4.cmml">⁣</mo><mrow id="S2.E2.m1.39.39.39.39.37.37.1.3.2.2" xref="S2.E2.m1.39.39.39.39.37.37.1.4.cmml"><mo stretchy="false" id="S2.E2.m1.39.39.39.39.37.37.1.3.2.2.1" xref="S2.E2.m1.39.39.39.39.37.37.1.4.cmml">(</mo><mo id="S2.E2.m1.39.39.39.39.37.37.1.1" xref="S2.E2.m1.39.39.39.39.37.37.1.1.cmml">-</mo><mo stretchy="false" id="S2.E2.m1.39.39.39.39.37.37.1.3.2.2.2" xref="S2.E2.m1.39.39.39.39.37.37.1.4.cmml">)</mo></mrow></mrow></msubsup></mrow></mrow></mrow></mrow></mrow></mtd></mtr><mtr id="S2.E2.m1.52.52.2d"><mtd id="S2.E2.m1.52.52.2e" xref="S2.E2.m1.51.51.1.1.1.cmml"/><mtd columnalign="left" id="S2.E2.m1.52.52.2f"><mrow id="S2.E2.m1.52.52.2.51.12.12.12"><mrow id="S2.E2.m1.52.52.2.51.12.12.12.1"><mi id="S2.E2.m1.52.52.2.51.12.12.12.1.1" xref="S2.E2.m1.51.51.1.1.1.cmml"/><mo id="S2.E2.m1.40.40.40.1.1.1" xref="S2.E2.m1.40.40.40.1.1.1.cmml">=</mo><mrow id="S2.E2.m1.52.52.2.51.12.12.12.1.2"><munder id="S2.E2.m1.52.52.2.51.12.12.12.1.2.1"><mo largeop="true" movablelimits="false" symmetric="true" id="S2.E2.m1.41.41.41.2.2.2" xref="S2.E2.m1.41.41.41.2.2.2.cmml">∑</mo><mi id="S2.E2.m1.42.42.42.3.3.3.1" xref="S2.E2.m1.42.42.42.3.3.3.1.cmml">n</mi></munder><mrow id="S2.E2.m1.52.52.2.51.12.12.12.1.2.2"><msub id="S2.E2.m1.52.52.2.51.12.12.12.1.2.2.2"><mi id="S2.E2.m1.43.43.43.4.4.4" xref="S2.E2.m1.43.43.43.4.4.4.cmml">ω</mi><mi id="S2.E2.m1.44.44.44.5.5.5.1" xref="S2.E2.m1.44.44.44.5.5.5.1.cmml">n</mi></msub><mo id="S2.E2.m1.52.52.2.51.12.12.12.1.2.2.1" xref="S2.E2.m1.51.51.1.1.1.cmml">⁢</mo><msubsup id="S2.E2.m1.52.52.2.51.12.12.12.1.2.2.3"><mi id="S2.E2.m1.45.45.45.6.6.6" xref="S2.E2.m1.45.45.45.6.6.6.cmml">X</mi><mi id="S2.E2.m1.46.46.46.7.7.7.1" xref="S2.E2.m1.46.46.46.7.7.7.1.cmml">n</mi><mo id="S2.E2.m1.47.47.47.8.8.8.1" xref="S2.E2.m1.47.47.47.8.8.8.1.cmml">†</mo></msubsup><mo id="S2.E2.m1.52.52.2.51.12.12.12.1.2.2.1a" xref="S2.E2.m1.51.51.1.1.1.cmml">⁢</mo><msub id="S2.E2.m1.52.52.2.51.12.12.12.1.2.2.4"><mi id="S2.E2.m1.48.48.48.9.9.9" xref="S2.E2.m1.48.48.48.9.9.9.cmml">X</mi><mi id="S2.E2.m1.49.49.49.10.10.10.1" xref="S2.E2.m1.49.49.49.10.10.10.1.cmml">n</mi></msub></mrow></mrow></mrow><mo id="S2.E2.m1.50.50.50.11.11.11" xref="S2.E2.m1.51.51.1.1.1.cmml">.</mo></mrow></mtd></mtr></mtable></math>, <math><mrow id="S2.p1.7.m5.2.2" xref="S2.p1.7.m5.2.2.cmml"><mi id="S2.p1.7.m5.2.2.3" xref="S2.p1.7.m5.2.2.3.cmml">r</mi><mo id="S2.p1.7.m5.2.2.4" xref="S2.p1.7.m5.2.2.4.cmml">=</mo><mrow id="S2.p1.7.m5.2.2.1.1" xref="S2.p1.7.m5.2.2.1.2.cmml"><mi id="S2.p1.7.m5.1.1" xref="S2.p1.7.m5.1.1.cmml">exp</mi><mo id="S2.p1.7.m5.2.2.1.1a" xref="S2.p1.7.m5.2.2.1.2.cmml">⁡</mo><mrow id="S2.p1.7.m5.2.2.1.1.1" xref="S2.p1.7.m5.2.2.1.2.cmml"><mo stretchy="false" id="S2.p1.7.m5.2.2.1.1.1.2" xref="S2.p1.7.m5.2.2.1.2.cmml">(</mo><mrow id="S2.p1.7.m5.2.2.1.1.1.1" xref="S2.p1.7.m5.2.2.1.1.1.1.cmml"><mo id="S2.p1.7.m5.2.2.1.1.1.1.1" xref="S2.p1.7.m5.2.2.1.1.1.1.1.cmml">-</mo><mrow id="S2.p1.7.m5.2.2.1.1.1.1.2" xref="S2.p1.7.m5.2.2.1.1.1.1.2.cmml"><mi id="S2.p1.7.m5.2.2.1.1.1.1.2.2" xref="S2.p1.7.m5.2.2.1.1.1.1.2.2.cmml">i</mi><mo id="S2.p1.7.m5.2.2.1.1.1.1.2.1" xref="S2.p1.7.m5.2.2.1.1.1.1.2.1.cmml">⁢</mo><mi id="S2.p1.7.m5.2.2.1.1.1.1.2.3" xref="S2.p1.7.m5.2.2.1.1.1.1.2.3.cmml">π</mi><mo id="S2.p1.7.m5.2.2.1.1.1.1.2.1a" xref="S2.p1.7.m5.2.2.1.1.1.1.2.1.cmml">⁢</mo><mi id="S2.p1.7.m5.2.2.1.1.1.1.2.4" xref="S2.p1.7.m5.2.2.1.1.1.1.2.4.cmml">α</mi></mrow></mrow><mo stretchy="false" id="S2.p1.7.m5.2.2.1.1.1.3" xref="S2.p1.7.m5.2.2.1.2.cmml">)</mo></mrow></mrow><mo id="S2.p1.7.m5.2.2.5" xref="S2.p1.7.m5.2.2.5.cmml">=</mo><mn id="S2.p1.7.m5.2.2.6" xref="S2.p1.7.m5.2.2.6.cmml">1</mn></mrow></math>, <math><mtable columnspacing="0pt" displaystyle="true" rowspacing="0pt" id="S2.E3.m1.69.69.8" xref="S2.E3.m1.65.65.4.cmml"><mtr id="S2.E3.m1.69.69.8a" xref="S2.E3.m1.65.65.4.cmml"><mtd columnalign="right" id="S2.E3.m1.69.69.8b" xref="S2.E3.m1.65.65.4.cmml"><mrow id="S2.E3.m1.5.5.5.5.5" xref="S2.E3.m1.65.65.4.cmml"><msub id="S2.E3.m1.5.5.5.5.5.7" xref="S2.E3.m1.65.65.4.cmml"><mi id="S2.E3.m1.1.1.1.1.1.1" xref="S2.E3.m1.1.1.1.1.1.1.cmml">H</mi><mi id="S2.E3.m1.2.2.2.2.2.2.1" xref="S2.E3.m1.2.2.2.2.2.2.1.cmml">couple</mi></msub><mo id="S2.E3.m1.5.5.5.5.5.6" xref="S2.E3.m1.65.65.4.cmml">⁢</mo><mrow id="S2.E3.m1.5.5.5.5.5.8" xref="S2.E3.m1.65.65.4.cmml"><mo stretchy="false" id="S2.E3.m1.3.3.3.3.3.3" xref="S2.E3.m1.65.65.4.cmml">(</mo><mi id="S2.E3.m1.4.4.4.4.4.4" xref="S2.E3.m1.4.4.4.4.4.4.cmml">γ</mi><mo stretchy="false" id="S2.E3.m1.5.5.5.5.5.5" xref="S2.E3.m1.65.65.4.cmml">)</mo></mrow></mrow></mtd><mtd columnalign="left" id="S2.E3.m1.69.69.8c" xref="S2.E3.m1.65.65.4.cmml"><mrow id="S2.E3.m1.67.67.6.63.34.29" xref="S2.E3.m1.65.65.4.cmml"><mi id="S2.E3.m1.67.67.6.63.34.29.30" xref="S2.E3.m1.65.65.4.cmml"/><mo id="S2.E3.m1.6.6.6.6.1.1" xref="S2.E3.m1.6.6.6.6.1.1.cmml">=</mo><mrow id="S2.E3.m1.67.67.6.63.34.29.29" xref="S2.E3.m1.65.65.4.cmml"><munder id="S2.E3.m1.67.67.6.63.34.29.29.3" xref="S2.E3.m1.65.65.4.cmml"><mo largeop="true" movablelimits="false" symmetric="true" id="S2.E3.m1.7.7.7.7.2.2" xref="S2.E3.m1.7.7.7.7.2.2.cmml">∑</mo><mrow id="S2.E3.m1.8.8.8.8.3.3.1" xref="S2.E3.m1.8.8.8.8.3.3.1.cmml"><mi id="S2.E3.m1.8.8.8.8.3.3.1.2" xref="S2.E3.m1.8.8.8.8.3.3.1.2.cmml">μ</mi><mo id="S2.E3.m1.8.8.8.8.3.3.1.1" xref="S2.E3.m1.8.8.8.8.3.3.1.1.cmml">⁢</mo><mi id="S2.E3.m1.8.8.8.8.3.3.1.3" xref="S2.E3.m1.8.8.8.8.3.3.1.3.cmml">ν</mi></mrow></munder><mrow id="S2.E3.m1.67.67.6.63.34.29.29.2" xref="S2.E3.m1.65.65.4.cmml"><msub id="S2.E3.m1.67.67.6.63.34.29.29.2.4" xref="S2.E3.m1.65.65.4.cmml"><mi mathvariant="normal" id="S2.E3.m1.9.9.9.9.4.4" xref="S2.E3.m1.9.9.9.9.4.4.cmml">Λ</mi><mi id="S2.E3.m1.10.10.10.10.5.5.1" xref="S2.E3.m1.10.10.10.10.5.5.1.cmml">γ</mi></msub><mo id="S2.E3.m1.67.67.6.63.34.29.29.2.3" xref="S2.E3.m1.65.65.4.cmml">⁢</mo><mrow id="S2.E3.m1.66.66.5.62.33.28.28.1.1.1" xref="S2.E3.m1.65.65.4.cmml"><mo stretchy="false" id="S2.E3.m1.11.11.11.11.6.6" xref="S2.E3.m1.65.65.4.cmml">(</mo><mrow id="S2.E3.m1.66.66.5.62.33.28.28.1.1.1.1" xref="S2.E3.m1.65.65.4.cmml"><mi id="S2.E3.m1.12.12.12.12.7.7" xref="S2.E3.m1.12.12.12.12.7.7.cmml">μ</mi><mo id="S2.E3.m1.66.66.5.62.33.28.28.1.1.1.1.1" xref="S2.E3.m1.65.65.4.cmml">⁢</mo><mi id="S2.E3.m1.13.13.13.13.8.8" xref="S2.E3.m1.13.13.13.13.8.8.cmml">ν</mi></mrow><mo stretchy="false" id="S2.E3.m1.14.14.14.14.9.9" xref="S2.E3.m1.65.65.4.cmml">)</mo></mrow><mo id="S2.E3.m1.67.67.6.63.34.29.29.2.3a" xref="S2.E3.m1.65.65.4.cmml">⁢</mo><mrow id="S2.E3.m1.67.67.6.63.34.29.29.2.2.1" xref="S2.E3.m1.65.65.4.cmml"><mo id="S2.E3.m1.15.15.15.15.10.10" xref="S2.E3.m1.65.65.4.cmml">(</mo><mrow id="S2.E3.m1.67.67.6.63.34.29.29.2.2.1.1" xref="S2.E3.m1.65.65.4.cmml"><mrow id="S2.E3.m1.67.67.6.63.34.29.29.2.2.1.1.1" xref="S2.E3.m1.65.65.4.cmml"><msubsup id="S2.E3.m1.67.67.6.63.34.29.29.2.2.1.1.1.2" xref="S2.E3.m1.65.65.4.cmml"><mi id="S2.E3.m1.16.16.16.16.11.11" xref="S2.E3.m1.16.16.16.16.11.11.cmml">X</mi><mi id="S2.E3.m1.17.17.17.17.12.12.1" xref="S2.E3.m1.17.17.17.17.12.12.1.cmml">γ</mi><mo id="S2.E3.m1.18.18.18.18.13.13.1" xref="S2.E3.m1.18.18.18.18.13.13.1.cmml">†</mo></msubsup><mo id="S2.E3.m1.67.67.6.63.34.29.29.2.2.1.1.1.1" xref="S2.E3.m1.65.65.4.cmml">⁢</mo><msubsup id="S2.E3.m1.67.67.6.63.34.29.29.2.2.1.1.1.3" xref="S2.E3.m1.65.65.4.cmml"><mi id="S2.E3.m1.19.19.19.19.14.14" xref="S2.E3.m1.19.19.19.19.14.14.cmml">a</mi><mi id="S2.E3.m1.20.20.20.20.15.15.1" xref="S2.E3.m1.20.20.20.20.15.15.1.cmml">μ</mi><mo id="S2.E3.m1.21.21.21.21.16.16.1" xref="S2.E3.m1.21.21.21.21.16.16.1.cmml">†</mo></msubsup><mo id="S2.E3.m1.67.67.6.63.34.29.29.2.2.1.1.1.1a" xref="S2.E3.m1.65.65.4.cmml">⁢</mo><msub id="S2.E3.m1.67.67.6.63.34.29.29.2.2.1.1.1.4" xref="S2.E3.m1.65.65.4.cmml"><mi id="S2.E3.m1.22.22.22.22.17.17" xref="S2.E3.m1.22.22.22.22.17.17.cmml">a</mi><mi id="S2.E3.m1.23.23.23.23.18.18.1" xref="S2.E3.m1.23.23.23.23.18.18.1.cmml">ν</mi></msub></mrow><mo id="S2.E3.m1.24.24.24.24.19.19" xref="S2.E3.m1.24.24.24.24.19.19.cmml">+</mo><mrow id="S2.E3.m1.67.67.6.63.34.29.29.2.2.1.1.2" xref="S2.E3.m1.65.65.4.cmml"><msub id="S2.E3.m1.67.67.6.63.34.29.29.2.2.1.1.2.2" xref="S2.E3.m1.65.65.4.cmml"><mi id="S2.E3.m1.25.25.25.25.20.20" xref="S2.E3.m1.25.25.25.25.20.20.cmml">X</mi><mi id="S2.E3.m1.26.26.26.26.21.21.1" xref="S2.E3.m1.26.26.26.26.21.21.1.cmml">γ</mi></msub><mo id="S2.E3.m1.67.67.6.63.34.29.29.2.2.1.1.2.1" xref="S2.E3.m1.65.65.4.cmml">⁢</mo><msubsup id="S2.E3.m1.67.67.6.63.34.29.29.2.2.1.1.2.3" xref="S2.E3.m1.65.65.4.cmml"><mi id="S2.E3.m1.27.27.27.27.22.22" xref="S2.E3.m1.27.27.27.27.22.22.cmml">a</mi><mi id="S2.E3.m1.28.28.28.28.23.23.1" xref="S2.E3.m1.28.28.28.28.23.23.1.cmml">ν</mi><mo id="S2.E3.m1.29.29.29.29.24.24.1" xref="S2.E3.m1.29.29.29.29.24.24.1.cmml">†</mo></msubsup><mo id="S2.E3.m1.67.67.6.63.34.29.29.2.2.1.1.2.1a" xref="S2.E3.m1.65.65.4.cmml">⁢</mo><msub id="S2.E3.m1.67.67.6.63.34.29.29.2.2.1.1.2.4" xref="S2.E3.m1.65.65.4.cmml"><mi id="S2.E3.m1.30.30.30.30.25.25" xref="S2.E3.m1.30.30.30.30.25.25.cmml">a</mi><mi id="S2.E3.m1.31.31.31.31.26.26.1" xref="S2.E3.m1.31.31.31.31.26.26.1.cmml">μ</mi></msub></mrow></mrow><mo id="S2.E3.m1.32.32.32.32.27.27" xref="S2.E3.m1.65.65.4.cmml">)</mo></mrow></mrow></mrow></mrow></mtd></mtr><mtr id="S2.E3.m1.69.69.8d" xref="S2.E3.m1.65.65.4.cmml"><mtd id="S2.E3.m1.69.69.8e" xref="S2.E3.m1.65.65.4.cmml"/><mtd columnalign="left" id="S2.E3.m1.69.69.8f" xref="S2.E3.m1.65.65.4.cmml"><mrow id="S2.E3.m1.69.69.8.65.29.29" xref="S2.E3.m1.65.65.4.cmml"><mo id="S2.E3.m1.33.33.33.1.1.1" xref="S2.E3.m1.33.33.33.1.1.1.cmml">+</mo><mrow id="S2.E3.m1.69.69.8.65.29.29.29" xref="S2.E3.m1.65.65.4.cmml"><munder id="S2.E3.m1.69.69.8.65.29.29.29.3" xref="S2.E3.m1.65.65.4.cmml"><mo largeop="true" movablelimits="false" symmetric="true" id="S2.E3.m1.34.34.34.2.2.2" xref="S2.E3.m1.34.34.34.2.2.2.cmml">∑</mo><mrow id="S2.E3.m1.35.35.35.3.3.3.1" xref="S2.E3.m1.35.35.35.3.3.3.1.cmml"><mi id="S2.E3.m1.35.35.35.3.3.3.1.2" xref="S2.E3.m1.35.35.35.3.3.3.1.2.cmml">μ</mi><mo id="S2.E3.m1.35.35.35.3.3.3.1.1" xref="S2.E3.m1.35.35.35.3.3.3.1.1.cmml">⁢</mo><mover accent="true" id="S2.E3.m1.35.35.35.3.3.3.1.3" xref="S2.E3.m1.35.35.35.3.3.3.1.3.cmml"><mi id="S2.E3.m1.35.35.35.3.3.3.1.3.2" xref="S2.E3.m1.35.35.35.3.3.3.1.3.2.cmml">ν</mi><mo stretchy="false" id="S2.E3.m1.35.35.35.3.3.3.1.3.1" xref="S2.E3.m1.35.35.35.3.3.3.1.3.1.cmml">¯</mo></mover></mrow></munder><mrow id="S2.E3.m1.69.69.8.65.29.29.29.2" xref="S2.E3.m1.65.65.4.cmml"><msub id="S2.E3.m1.69.69.8.65.29.29.29.2.4" xref="S2.E3.m1.65.65.4.cmml"><mi mathvariant="normal" id="S2.E3.m1.36.36.36.4.4.4" xref="S2.E3.m1.36.36.36.4.4.4.cmml">Λ</mi><mover accent="true" id="S2.E3.m1.37.37.37.5.5.5.1" xref="S2.E3.m1.37.37.37.5.5.5.1.cmml"><mi id="S2.E3.m1.37.37.37.5.5.5.1.2" xref="S2.E3.m1.37.37.37.5.5.5.1.2.cmml">γ</mi><mo stretchy="false" id="S2.E3.m1.37.37.37.5.5.5.1.1" xref="S2.E3.m1.37.37.37.5.5.5.1.1.cmml">¯</mo></mover></msub><mo id="S2.E3.m1.69.69.8.65.29.29.29.2.3" xref="S2.E3.m1.65.65.4.cmml">⁢</mo><mrow id="S2.E3.m1.68.68.7.64.28.28.28.1.1.1" xref="S2.E3.m1.65.65.4.cmml"><mo stretchy="false" id="S2.E3.m1.38.38.38.6.6.6" xref="S2.E3.m1.65.65.4.cmml">(</mo><mrow id="S2.E3.m1.68.68.7.64.28.28.28.1.1.1.1" xref="S2.E3.m1.65.65.4.cmml"><mi id="S2.E3.m1.39.39.39.7.7.7" xref="S2.E3.m1.39.39.39.7.7.7.cmml">μ</mi><mo id="S2.E3.m1.68.68.7.64.28.28.28.1.1.1.1.1" xref="S2.E3.m1.65.65.4.cmml">⁢</mo><mover accent="true" id="S2.E3.m1.40.40.40.8.8.8" xref="S2.E3.m1.40.40.40.8.8.8.cmml"><mi id="S2.E3.m1.40.40.40.8.8.8.2" xref="S2.E3.m1.40.40.40.8.8.8.2.cmml">ν</mi><mo stretchy="false" id="S2.E3.m1.40.40.40.8.8.8.1" xref="S2.E3.m1.40.40.40.8.8.8.1.cmml">¯</mo></mover></mrow><mo stretchy="false" id="S2.E3.m1.41.41.41.9.9.9" xref="S2.E3.m1.65.65.4.cmml">)</mo></mrow><mo id="S2.E3.m1.69.69.8.65.29.29.29.2.3a" xref="S2.E3.m1.65.65.4.cmml">⁢</mo><mrow id="S2.E3.m1.69.69.8.65.29.29.29.2.2.1" xref="S2.E3.m1.65.65.4.cmml"><mo id="S2.E3.m1.42.42.42.10.10.10" xref="S2.E3.m1.65.65.4.cmml">(</mo><mrow id="S2.E3.m1.69.69.8.65.29.29.29.2.2.1.1" xref="S2.E3.m1.65.65.4.cmml"><mrow id="S2.E3.m1.69.69.8.65.29.29.29.2.2.1.1.1" xref="S2.E3.m1.65.65.4.cmml"><msubsup id="S2.E3.m1.69.69.8.65.29.29.29.2.2.1.1.1.2" xref="S2.E3.m1.65.65.4.cmml"><mi id="S2.E3.m1.43.43.43.11.11.11" xref="S2.E3.m1.43.43.43.11.11.11.cmml">X</mi><mover accent="true" id="S2.E3.m1.44.44.44.12.12.12.1" xref="S2.E3.m1.44.44.44.12.12.12.1.cmml"><mi id="S2.E3.m1.44.44.44.12.12.12.1.2" xref="S2.E3.m1.44.44.44.12.12.12.1.2.cmml">γ</mi><mo stretchy="false" id="S2.E3.m1.44.44.44.12.12.12.1.1" xref="S2.E3.m1.44.44.44.12.12.12.1.1.cmml">¯</mo></mover><mo id="S2.E3.m1.45.45.45.13.13.13.1" xref="S2.E3.m1.45.45.45.13.13.13.1.cmml">†</mo></msubsup><mo id="S2.E3.m1.69.69.8.65.29.29.29.2.2.1.1.1.1" xref="S2.E3.m1.65.65.4.cmml">⁢</mo><msubsup id="S2.E3.m1.69.69.8.65.29.29.29.2.2.1.1.1.3" xref="S2.E3.m1.65.65.4.cmml"><mi id="S2.E3.m1.46.46.46.14.14.14" xref="S2.E3.m1.46.46.46.14.14.14.cmml">a</mi><mi id="S2.E3.m1.47.47.47.15.15.15.1" xref="S2.E3.m1.47.47.47.15.15.15.1.cmml">μ</mi><mo id="S2.E3.m1.48.48.48.16.16.16.1" xref="S2.E3.m1.48.48.48.16.16.16.1.cmml">†</mo></msubsup><mo id="S2.E3.m1.69.69.8.65.29.29.29.2.2.1.1.1.1a" xref="S2.E3.m1.65.65.4.cmml">⁢</mo><msub id="S2.E3.m1.69.69.8.65.29.29.29.2.2.1.1.1.4" xref="S2.E3.m1.65.65.4.cmml"><mi id="S2.E3.m1.49.49.49.17.17.17" xref="S2.E3.m1.49.49.49.17.17.17.cmml">a</mi><mover accent="true" id="S2.E3.m1.50.50.50.18.18.18.1" xref="S2.E3.m1.50.50.50.18.18.18.1.cmml"><mi id="S2.E3.m1.50.50.50.18.18.18.1.2" xref="S2.E3.m1.50.50.50.18.18.18.1.2.cmml">ν</mi><mo stretchy="false" id="S2.E3.m1.50.50.50.18.18.18.1.1" xref="S2.E3.m1.50.50.50.18.18.18.1.1.cmml">¯</mo></mover></msub></mrow><mo id="S2.E3.m1.51.51.51.19.19.19" xref="S2.E3.m1.51.51.51.19.19.19.cmml">+</mo><mrow id="S2.E3.m1.69.69.8.65.29.29.29.2.2.1.1.2" xref="S2.E3.m1.65.65.4.cmml"><msub id="S2.E3.m1.69.69.8.65.29.29.29.2.2.1.1.2.2" xref="S2.E3.m1.65.65.4.cmml"><mi id="S2.E3.m1.52.52.52.20.20.20" xref="S2.E3.m1.52.52.52.20.20.20.cmml">X</mi><mover accent="true" id="S2.E3.m1.53.53.53.21.21.21.1" xref="S2.E3.m1.53.53.53.21.21.21.1.cmml"><mi id="S2.E3.m1.53.53.53.21.21.21.1.2" xref="S2.E3.m1.53.53.53.21.21.21.1.2.cmml">γ</mi><mo stretchy="false" id="S2.E3.m1.53.53.53.21.21.21.1.1" xref="S2.E3.m1.53.53.53.21.21.21.1.1.cmml">¯</mo></mover></msub><mo id="S2.E3.m1.69.69.8.65.29.29.29.2.2.1.1.2.1" xref="S2.E3.m1.65.65.4.cmml">⁢</mo><msubsup id="S2.E3.m1.69.69.8.65.29.29.29.2.2.1.1.2.3" xref="S2.E3.m1.65.65.4.cmml"><mi id="S2.E3.m1.54.54.54.22.22.22" xref="S2.E3.m1.54.54.54.22.22.22.cmml">a</mi><mover accent="true" id="S2.E3.m1.55.55.55.23.23.23.1" xref="S2.E3.m1.55.55.55.23.23.23.1.cmml"><mi id="S2.E3.m1.55.55.55.23.23.23.1.2" xref="S2.E3.m1.55.55.55.23.23.23.1.2.cmml">ν</mi><mo stretchy="false" id="S2.E3.m1.55.55.55.23.23.23.1.1" xref="S2.E3.m1.55.55.55.23.23.23.1.1.cmml">¯</mo></mover><mo id="S2.E3.m1.56.56.56.24.24.24.1" xref="S2.E3.m1.56.56.56.24.24.24.1.cmml">†</mo></msubsup><mo id="S2.E3.m1.69.69.8.65.29.29.29.2.2.1.1.2.1a" xref="S2.E3.m1.65.65.4.cmml">⁢</mo><msub id="S2.E3.m1.69.69.8.65.29.29.29.2.2.1.1.2.4" xref="S2.E3.m1.65.65.4.cmml"><mi id="S2.E3.m1.57.57.57.25.25.25" xref="S2.E3.m1.57.57.57.25.25.25.cmml">a</mi><mi id="S2.E3.m1.58.58.58.26.26.26.1" xref="S2.E3.m1.58.58.58.26.26.26.1.cmml">μ</mi></msub></mrow></mrow><mo id="S2.E3.m1.59.59.59.27.27.27" xref="S2.E3.m1.65.65.4.cmml">)</mo></mrow></mrow></mrow></mrow></mtd></mtr><mtr id="S2.E3.m1.69.69.8g" xref="S2.E3.m1.65.65.4.cmml"><mtd id="S2.E3.m1.69.69.8h" xref="S2.E3.m1.65.65.4.cmml"/><mtd columnalign="left" id="S2.E3.m1.69.69.8i" xref="S2.E3.m1.65.65.4.cmml"><mrow id="S2.E3.m1.61.61.61.2.2" xref="S2.E3.m1.65.65.4.cmml"><mo id="S2.E3.m1.60.60.60.1.1.1" xref="S2.E3.m1.65.65.4.cmml">+</mo><mtext id="S2.E3.m1.61.61.61.2.2.2" xref="S2.E3.m1.61.61.61.2.2.2a.cmml">sig. conj.</mtext></mrow></mtd></mtr></mtable></math>, <math><mrow id="S2.p2.3.m3.1.1" xref="S2.p2.3.m3.1.1.cmml"><mrow id="S2.p2.3.m3.1.1.3" xref="S2.p2.3.m3.1.1.3.cmml"><mn id="S2.p2.3.m3.1.1.3.2" xref="S2.p2.3.m3.1.1.3.2.cmml">1</mn><mo id="S2.p2.3.m3.1.1.3.1" xref="S2.p2.3.m3.1.1.3.1.cmml">⁢</mo><mi mathvariant="normal" id="S2.p2.3.m3.1.1.3.3" xref="S2.p2.3.m3.1.1.3.3.cmml">q</mi><mo id="S2.p2.3.m3.1.1.3.1a" xref="S2.p2.3.m3.1.1.3.1.cmml">⁢</mo><mi mathvariant="normal" id="S2.p2.3.m3.1.1.3.4" xref="S2.p2.3.m3.1.1.3.4.cmml">p</mi></mrow><mo id="S2.p2.3.m3.1.1.2" xref="S2.p2.3.m3.1.1.2.cmml">⊗</mo><msup id="S2.p2.3.m3.1.1.1" xref="S2.p2.3.m3.1.1.1.cmml"><mrow id="S2.p2.3.m3.1.1.1.1.1" xref="S2.p2.3.m3.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S2.p2.3.m3.1.1.1.1.1.2" xref="S2.p2.3.m3.1.1.1.1.1.1.cmml">(</mo><mrow id="S2.p2.3.m3.1.1.1.1.1.1" xref="S2.p2.3.m3.1.1.1.1.1.1.cmml"><mi id="S2.p2.3.m3.1.1.1.1.1.1.2" xref="S2.p2.3.m3.1.1.1.1.1.1.2.cmml">γ</mi><mo id="S2.p2.3.m3.1.1.1.1.1.1.1" xref="S2.p2.3.m3.1.1.1.1.1.1.1.cmml">⁢</mo><mtext id="S2.p2.3.m3.1.1.1.1.1.1.3" xref="S2.p2.3.m3.1.1.1.1.1.1.3a.cmml"> or </mtext><mo id="S2.p2.3.m3.1.1.1.1.1.1.1a" xref="S2.p2.3.m3.1.1.1.1.1.1.1.cmml">⁢</mo><mover accent="true" id="S2.p2.3.m3.1.1.1.1.1.1.4" xref="S2.p2.3.m3.1.1.1.1.1.1.4.cmml"><mi id="S2.p2.3.m3.1.1.1.1.1.1.4.2" xref="S2.p2.3.m3.1.1.1.1.1.1.4.2.cmml">γ</mi><mo stretchy="false" id="S2.p2.3.m3.1.1.1.1.1.1.4.1" xref="S2.p2.3.m3.1.1.1.1.1.1.4.1.cmml">¯</mo></mover></mrow><mo stretchy="false" id="S2.p2.3.m3.1.1.1.1.1.3" xref="S2.p2.3.m3.1.1.1.1.1.1.cmml">)</mo></mrow><mi id="S2.p2.3.m3.1.1.1.3" xref="S2.p2.3.m3.1.1.1.3.cmml">n</mi></msup></mrow></math>, <math><mrow id="S2.p2.7.m7.1.1" xref="S2.p2.7.m7.1.1.cmml"><msub id="S2.p2.7.m7.1.1.1" xref="S2.p2.7.m7.1.1.1.cmml"><mrow id="S2.p2.7.m7.1.1.1.1.1" xref="S2.p2.7.m7.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S2.p2.7.m7.1.1.1.1.1.2" xref="S2.p2.7.m7.1.1.1.1.1.1.cmml">(</mo><mrow id="S2.p2.7.m7.1.1.1.1.1.1" xref="S2.p2.7.m7.1.1.1.1.1.1.cmml"><mn id="S2.p2.7.m7.1.1.1.1.1.1.2" xref="S2.p2.7.m7.1.1.1.1.1.1.2.cmml">1</mn><mo id="S2.p2.7.m7.1.1.1.1.1.1.1" xref="S2.p2.7.m7.1.1.1.1.1.1.1.cmml">⁢</mo><mi mathvariant="normal" id="S2.p2.7.m7.1.1.1.1.1.1.3" xref="S2.p2.7.m7.1.1.1.1.1.1.3.cmml">q</mi><mo id="S2.p2.7.m7.1.1.1.1.1.1.1a" xref="S2.p2.7.m7.1.1.1.1.1.1.1.cmml">⁢</mo><mi mathvariant="normal" id="S2.p2.7.m7.1.1.1.1.1.1.4" xref="S2.p2.7.m7.1.1.1.1.1.1.4.cmml">p</mi></mrow><mo stretchy="false" id="S2.p2.7.m7.1.1.1.1.1.3" xref="S2.p2.7.m7.1.1.1.1.1.1.cmml">)</mo></mrow><mrow id="S2.p2.7.m7.1.1.1.3" xref="S2.p2.7.m7.1.1.1.3.cmml"><mi id="S2.p2.7.m7.1.1.1.3.2" xref="S2.p2.7.m7.1.1.1.3.2.cmml">r</mi><mo id="S2.p2.7.m7.1.1.1.3.1" xref="S2.p2.7.m7.1.1.1.3.1.cmml">=</mo><mrow id="S2.p2.7.m7.1.1.1.3.3" xref="S2.p2.7.m7.1.1.1.3.3.cmml"><mo id="S2.p2.7.m7.1.1.1.3.3.1" xref="S2.p2.7.m7.1.1.1.3.3.1.cmml">±</mo><mi id="S2.p2.7.m7.1.1.1.3.3.2" xref="S2.p2.7.m7.1.1.1.3.3.2.cmml">i</mi></mrow></mrow></msub><mo id="S2.p2.7.m7.1.1.2" xref="S2.p2.7.m7.1.1.2.cmml">⊗</mo><mi id="S2.p2.7.m7.1.1.3" xref="S2.p2.7.m7.1.1.3.cmml">γ</mi></mrow></math>, <math><mrow id="S2.p2.8.m8.1.1" xref="S2.p2.8.m8.1.1.cmml"><msub id="S2.p2.8.m8.1.1.1" xref="S2.p2.8.m8.1.1.1.cmml"><mrow id="S2.p2.8.m8.1.1.1.1.1" xref="S2.p2.8.m8.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S2.p2.8.m8.1.1.1.1.1.2" xref="S2.p2.8.m8.1.1.1.1.1.1.cmml">(</mo><mrow id="S2.p2.8.m8.1.1.1.1.1.1" xref="S2.p2.8.m8.1.1.1.1.1.1.cmml"><mn id="S2.p2.8.m8.1.1.1.1.1.1.2" xref="S2.p2.8.m8.1.1.1.1.1.1.2.cmml">1</mn><mo id="S2.p2.8.m8.1.1.1.1.1.1.1" xref="S2.p2.8.m8.1.1.1.1.1.1.1.cmml">⁢</mo><mi mathvariant="normal" id="S2.p2.8.m8.1.1.1.1.1.1.3" xref="S2.p2.8.m8.1.1.1.1.1.1.3.cmml">q</mi><mo id="S2.p2.8.m8.1.1.1.1.1.1.1a" xref="S2.p2.8.m8.1.1.1.1.1.1.1.cmml">⁢</mo><mi mathvariant="normal" id="S2.p2.8.m8.1.1.1.1.1.1.4" xref="S2.p2.8.m8.1.1.1.1.1.1.4.cmml">p</mi></mrow><mo stretchy="false" id="S2.p2.8.m8.1.1.1.1.1.3" xref="S2.p2.8.m8.1.1.1.1.1.1.cmml">)</mo></mrow><mrow id="S2.p2.8.m8.1.1.1.3" xref="S2.p2.8.m8.1.1.1.3.cmml"><mi id="S2.p2.8.m8.1.1.1.3.2" xref="S2.p2.8.m8.1.1.1.3.2.cmml">r</mi><mo id="S2.p2.8.m8.1.1.1.3.1" xref="S2.p2.8.m8.1.1.1.3.1.cmml">=</mo><mrow id="S2.p2.8.m8.1.1.1.3.3" xref="S2.p2.8.m8.1.1.1.3.3.cmml"><mo id="S2.p2.8.m8.1.1.1.3.3.1" xref="S2.p2.8.m8.1.1.1.3.3.1.cmml">∓</mo><mi id="S2.p2.8.m8.1.1.1.3.3.2" xref="S2.p2.8.m8.1.1.1.3.3.2.cmml">i</mi></mrow></mrow></msub><mo id="S2.p2.8.m8.1.1.2" xref="S2.p2.8.m8.1.1.2.cmml">⊗</mo><mover accent="true" id="S2.p2.8.m8.1.1.3" xref="S2.p2.8.m8.1.1.3.cmml"><mi id="S2.p2.8.m8.1.1.3.2" xref="S2.p2.8.m8.1.1.3.2.cmml">γ</mi><mo stretchy="false" id="S2.p2.8.m8.1.1.3.1" xref="S2.p2.8.m8.1.1.3.1.cmml">¯</mo></mover></mrow></math>

Correct Categorie: nucl-th

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1409.6551

Formulas:

1-

(2 + ε, O (n^{0.5 + ε}))

2-

(1 + ε, O ({| R |}^{ε}))

3-

(α + ε, O (n^{0.5 + ε}))

4-

G = (V, E)

5-

G = (V, E)

6-

{\bar{ℓ}}_{H} (u, v)

7-

O (\log n \log L)

8-

Ω (2^{\log^{1 - ε} n})

9-

O (n \log L)

10-

(2 + ε, O (n^{1 / 2 + ε}))

Formulas (html):

Correct Categorie: cs

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/1210.1003

Formulas:

1-

PG (n, p^{t})

2-

PG (n, p^{t})

3-

(t / e - 1)

4-

p > 5 (t / e) - 11

5-

PG (n, p^{t})

6-

p > 5 t - 11

7-

V (n + 1, q)

8-

PG (n, q)

9-

PG (n, q)

10-

PG (n, q)

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/1005.5256

Formulas:

1-

g g \to t \bar{t} g g

2-

g g \to t \bar{t} g g

3-

p p \to t \bar{t} + b \bar{b}

4-

V + 3 j e t

5-

q q \to b \bar{b} b \bar{b}

6-

p p \to t \bar{t} + 2 j e t s

7-

g g \to t \bar{t} g g

8-

g g \to t \bar{t} g g

9-

{(T^{α_{1}} T^{α_{2}} T^{α_{3}} T^{α_{4}})}_{f_{1} f_{2}}

10-

T r {T^{α_{1}} T^{α_{2}}} {(T^{α_{3}} T^{α_{4}})}_{f_{1} f_{2}}

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/1701.04149

Formulas:

1-

1 + 2 \to 3 + 4

2-

σ {(E)}_{12}

3-

{⟨ σ v ⟩}_{12} = \sqrt{\frac{8}{π μ_{12} {(k T)}^{3}}} \int_{0}^{\infty} σ {(E)}_{12} E \exp (- \frac{E}{k T}) 𝑑 E,

4-

f_{q} (𝐯) = B_{q} {(\frac{m}{2 π k T})}^{3 / 2} {[1 - (q - 1) \frac{m 𝐯^{2}}{2 k T}]}^{\frac{1}{q - 1}},

5-

1 + 2 \to 3 + 4

6-

{⟨ σ v ⟩}_{12} = B_{q} \sqrt{\frac{8}{π μ_{12}}} \times \frac{1}{{(k T)}^{3 / 2}} \times \int_{0}^{E_{\max}} σ_{12} (E) E {[1 - (q - 1) \frac{E}{k T}]}^{\frac{1}{q - 1}} 𝑑 E,

7-

\frac{k T}{q - 1}

8-

1 + 2 \to 3 + 4

9-

3 + 4 \to 1 + 2

10-

(- \frac{Q}{k T})

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: nucl-th

Result: incorrect

Paper: https://arxiv.org/abs/1001.0703

Formulas:

1-

N - 2 N_{I}

2-

ρ_{i} = A_{α} δ_{i}

3-

N_{I} < i \leq N - N_{I}

4-

N - N_{I} < i \leq N

5-

p_{a b} = δ_{a} (1 - δ_{b}) \exp (- V_{0} + Δ V_{a}) .

6-

\exp (- V_{0})

7-

\exp (Δ V_{a})

8-

δ_{o} = 10^{- 4}

9-

0 \to + V_{\max} \to 0 \to - V_{\max} \to 0

10-

τ_{\max} = n s

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/hep-ph/0404203

Formulas:

1-

a_{π d} = [- 0.0261 (\pm 0.0005) + i 0.0063 (\pm 0.0007)] m_{π}^{- 1}

2-

π^{-} d \to n n

3-

π^{-} d \to γ n n

4-

π^{-} d \to π^{0} n n

5-

(\partial^{2} + m^{2}) φ = 0,

6-

\partial_{t}^{2} φ = (\nabla^{2} - m^{2}) φ,

7-

\partial_{t} = \partial / \partial t

8-

g_{00} = + 1, g_{11} = g_{22} = g_{33} = - 1

9-

θ = \frac{1}{2} (φ + \frac{i}{m} \partial_{t} φ), χ = \frac{1}{2} (φ - \frac{i}{m} \partial_{t} φ) .

10-

φ \sim e^{- i m t}

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

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

Formulas:

1-

γ = E / m c^{2} = 10^{5}

2-

\vec{x} = \vec{β} c t

3-

γ \sim 10^{3} - 10^{4}

4-

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

5-

d^{2} S_{o} / d Ω d ω

6-

ϵ_{1, 2} = 1 - ω_{1, 2}^{2} / ω^{2}

7-

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

8-

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

9-

ω_{1, 2} ≪ ω

10-

ω ≲ γ ω_{1}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: gr-qc

Result: incorrect

Paper: https://arxiv.org/abs/1612.04146

Formulas:

1-

O (1 / \log \log d)

2-

K := {x \in ℝ^{n} : g_{i}^{K} (x) \geq 0, i = 1, \dots, n_{K}}

3-

{(g_{i}^{K})}_{i} \subset ℝ [x]

4-

vol K := \int_{K} 𝑑 x .

5-

X := {x \in ℝ^{n} : g_{i}^{X} (x) \geq 0, i = 1, \dots, n_{X}}

6-

{(g_{i}^{X})}_{i} \subset ℝ [x]

7-

K \subset X \subset B_{n} := {x \in ℝ^{n} : {∥ x ∥}_{2} \leq 1}

8-

g_{0}^{K} := g_{0}^{X} := 1

9-

1 - \sum_{k = 1}^{n} x_{k}^{2}

10-

Q_{d} (K) := {\sum_{i = 0}^{n_{K}} g_{i}^{K} s_{i}^{K} : s_{i}^{K} \in Σ [x], \deg (g_{i}^{K} s_{i}^{K}) \leq 2 ⌊ \frac{d}{2} ⌋}

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/hep-lat/9908004

Formulas:

1-

⟨ \hat{A} ⟩ = Tr (\hat{A} \hat{ρ})

2-

\hat{ρ} = \sum_{i} p_{i} | ψ_{i} ⟩ ⟨ ψ_{i} |

3-

\sum_{i} p_{i} = 1

4-

[\hat{H}, \hat{ρ}] = 0

5-

\hat{ρ} = F (\hat{H})

6-

\hat{ρ} = \sum_{i} F (E_{i}) | ψ_{i} ⟩ ⟨ ψ_{i} |

7-

Tr e^{- β \hat{H}} < \infty

8-

e^{β E} F (E)

9-

0 < β < β_{+}

10-

Tr [\hat{A} e^{- β \hat{H}}] < \infty

Formulas (html):

Correct Categorie: hep-lat

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0606283

Formulas:

1-

n = 3 \to n = 2

2-

\frac{d E M}{d \log T} = \sum_{i} η δ (\log T - \log T_{i}),

3-

\log (T) = 6.8

4-

2 π D^{2} \times 10^{12}

5-

X^{2} = - 2 \ln (L),

6-

1.8 π D^{2} \times 10^{13}

7-

\log (T) = 6.3

8-

\log (T) = 7.4

9-

N_{H} = 1.8 \times 10^{18}

10-

\log (T) = 6.8

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/9811203

Formulas:

1-

γ = {(1 - β^{2})}^{- \frac{1}{2}}

2-

S_{obs} = S_{rest} {[γ (1 - β \cos θ)]}^{- (m + α)}

3-

p^{'} = p {[γ (1 - β \cos θ)]}^{- (m + α)}

4-

p_{c}^{'} = p_{c} {{[γ (1 - β_{c} \cos θ)]}^{- (m + α)} + {[γ (1 + β_{c} \cos θ)]}^{- (m + α)}}

5-

p_{c}^{'} \propto {(L \sin θ)}^{1.6 \pm 0.4}

6-

p_{c}^{'} = k_{c, l} L^{a} {{[γ (1 - β_{c} \cos θ)]}^{- (m + α)} + {[γ (1 + β_{c} \cos θ)]}^{- (m + α)}}

7-

k_{c, l} \sim 2.5 \times 10^{- 7}

8-

β_{j} = {0.62}_{- 0.1}^{+ 0.04}

9-

p_{j}^{'} = p_{j} {[γ_{j} (1 - β_{j} \cos θ)]}^{- (3 + 2 α)} {(\sin θ)}^{1 + α}

10-

θ_{c} = (π / 2) - θ_{j}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/math/0601220

Formulas:

1-

f^{'''} + α f f^{''} - β f^{', 2} = 0

2-

f (0) = - γ, f^{'} (\infty) = 0 and f^{'} (0) = 1,

3-

f (0) = - γ, f^{'} (\infty) = 0 and f^{''} (0) = - 1 .

4-

α = \frac{m + 1}{2}

5-

β = 2 m + 1

6-

\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} = 0,

7-

u = - \frac{k}{μ} (\frac{\partial p}{\partial x} + ρ g),

8-

v = - \frac{k}{μ} \frac{\partial p}{\partial y},

9-

u \frac{\partial T}{\partial x} + v \frac{\partial T}{\partial y} = λ (\frac{\partial^{2} T}{\partial x^{2}} + \frac{\partial^{2} T}{\partial y^{2}}),

10-

ρ = ρ_{\infty} (1 - β (T - T_{\infty}))

Formulas (html):

Correct Categorie: math

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1805.07942

Formulas:

1-

j = j_{↑} + j_{↓}

2-

U^{\pm} = U \mp Δ

3-

\approx 2 μ_{B} B

4-

R_{NL} \equiv V_{NL} / I

5-

R_{NL} = R_{0} + β (μ_{0} H) E_{Z}^{2}

6-

E_{Z} = g μ_{B} B_{Z} = g μ_{B} (B_{ex} + μ_{0} H)

7-

μ_{0} H \sim 3.8

8-

μ_{0} H > 20

9-

2 λ_{c, v}

10-

H_{SO} = 𝛀 (𝒌) \cdot 𝒔

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0401267

Formulas:

1-

μ \sum_{i} f_{i} \int 𝑑 𝐫 {| {\dot{Ψ}}_{i} (𝐫) |}^{2} + \frac{1}{2} \sum_{I} M_{I} {\dot{𝐑}}_{I}^{2} -

2-

E_{K S} [{Ψ_{i}}, 𝐑_{I}] +

3-

\sum_{i j} Λ_{i j} (\int 𝑑 𝐫 Ψ_{i}^{*} (𝐫) Ψ_{j} (𝐫) - δ_{i j}) .

4-

Ψ_{i} (r)

5-

\int Ψ_{i}^{*} Ψ_{j} = δ_{i j}

6-

μ {\ddot{Ψ}}_{i} (𝐫, t) = - \frac{δ E}{δ Ψ_{i}^{*} (𝐫, t)} + \sum_{j} Λ_{i j} Ψ_{j} (𝐫, t)

7-

M_{I} {\ddot{𝐑}}_{I} = - \frac{\partial E}{\partial 𝐑_{I} (t)} .

8-

ω_{i j} = {[\frac{2 (ϵ_{j} - ϵ_{i})}{μ}]}^{1 / 2},

9-

k_{B} T \sim 200

10-

ℏ ω ≫ k_{B} T .

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1001.0687

Formulas:

1-

a = λ e | δ B | / m c^{2}

2-

γ < 10^{6} {(n / 1 {cm}^{- 3})}^{- 1 / 6} {\bar{γ}}^{1 / 6}

3-

ℏ ω_{\max} < 40 Max (a, 1) {(n / 1 {cm}^{- 3})}^{1 / 6} {\bar{γ}}^{- 1 / 6} eV

4-

a < a_{crit} \sim 10^{6}

5-

\sim 150 η {(v_{s} / c)}^{2}

6-

ω_{p} = \sqrt{4 π n e^{2} / \bar{γ} m}

7-

\begin{matrix} σ_{u} = B_{u}^{2} / (4 π n_{u} m c^{2}) \\ σ_{d} = B_{d}^{2} / (4 π \bar{γ} n_{d} m c^{2}) \end{matrix}

8-

B_{d} / B_{u} \sim n_{d} / n_{u} \sim 3 \bar{γ}

9-

σ_{u} < 10^{- 3}

10-

ℓ_{w} c / ω_{p}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1510.00096

Formulas:

1-

ρ_{h o t}

2-

1.8 - 2.4 \times 10^{6}

3-

ρ_{h o t}

4-

10^{- 4} c m^{- 3}

5-

ρ_{h o t}

6-

10^{- 4} c m^{- 3}

7-

10^{- 4} c m^{- 3}

8-

2 \times 10^{9} M_{⊙}

9-

V_{L S R}

10-

R e = 445 \times f_{μ}^{- 1},

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/quant-ph/9612012

Formulas:

1-

σ_{1}, σ_{2} ≪ | ω_{1} - ω_{2} |

2-

ω_{0} \approx ω_{1, 2}

3-

ω_{0, 1, 2} \approx 10^{15}

4-

Δ t_{A, B} \geq 1 / σ_{1, 2}

5-

Δ t \approx 1 / σ_{\infty} \to 0

6-

γ_{1, 2} \approx σ_{1, 2}

7-

δ ω_{12} = | ω_{1} - ω_{2} |

8-

δ ω_{12} > 3 (σ_{1} + σ_{2})

9-

1 / δ ω_{12}

10-

Δ t_{\infty} \approx 1 / σ_{\infty} \to 0

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1308.0973

Formulas:

1-

V = β_{v} c

2-

(r, ϑ, φ)

3-

= β_{v}^{2} B_{L} \frac{r_{L}^{2}}{r^{2}} \tanh (Ψ_{s} / Δ)

4-

= - β_{v} B_{L} \frac{r_{L}}{r} \sin ϑ \tanh (Ψ_{s} / Δ)

5-

= - β_{v}^{2} c B_{L} \frac{r_{L}}{r} \sin ϑ \tanh (Ψ_{s} / Δ)

6-

r_{L} = c / Ω

7-

\nabla \times 𝐄 = - \partial_{t} 𝐁

8-

Ψ_{s} = \cos ϑ \cos χ + \sin ϑ \sin χ \cos [φ - Ω (t - \frac{r}{β_{v} c})]

9-

β_{v} = V / c

10-

= β_{v} c \frac{\sin^{2} ϑ}{\sin^{2} ϑ + β_{v}^{2} r_{L}^{2} / r^{2}}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1705.05753

Formulas:

1-

L (ℏ ω)

2-

L (ℏ ω) = C ω^{3} A (ℏ ω),

3-

A (ℏ ω)

4-

S (ℏ ω)

5-

S (ℏ ω)

6-

S (ℏ ω) = \sum_{k} S_{k} δ (ℏ ω - ℏ ω_{k}),

7-

S_{k} = \frac{ω_{k}}{2 ℏ} q_{k}^{2},

8-

q_{k} = \sum_{a i} m_{a}^{1 / 2} (R_{e, a i} - R_{g, a i}) Δ r_{k, a i},

9-

i = x, y, z

10-

R_{g / e, a i}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1202.2820

Formulas:

1-

𝖶 [1] = 𝖥𝖯𝖳

2-

d (x, y)

3-

S = {s_{1}, \dots, s_{n}}

4-

d (s, s_{i}) \leq d

5-

S = {s_{1}, \dots, s_{n}}

6-

\max {d (s, s_{i}) ∣ s_{i} \in S^{*}}

7-

S = {s_{1}, \dots, s_{n}}

8-

{t \in [ℓ] ∣ \exists s_{i}^{*}, s_{j}^{*} \in S^{*} : s_{i}^{*} (t) \neq s_{j}^{*} (t)}

9-

𝖶 [1] = 𝖥𝖯𝖳

10-

d (s, s_{i}) \geq d

Formulas (html):

Correct Categorie: cs

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/1204.4060

Formulas:

1-

E_{θ} = - \partial_{θ} ϕ = 0

2-

v_{r} = E_{θ} / B = 0

3-

k_{∥} \approx k_{⟂} \approx 0

4-

\frac{ι}{2 π} (a) = 1.65

5-

\frac{ι}{2 π} (0) = 1.55

6-

M = U Σ V^{†},

7-

U U^{†} = V V^{†} = I

8-

(σ_{1} \geq σ_{2} \geq \dots)

9-

{𝐮^{α}}_{α = 1 \dots m}

10-

{𝐯^{α}}_{α = 1 \dots n}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/1612.06812

Formulas:

1-

| 0^{n} ⟩ = \frac{1}{\sqrt{2}} ({| + ⟩}^{\otimes n} + {| - ⟩}^{\otimes n})

2-

| 1^{n} ⟩ = \frac{1}{\sqrt{2}} ({| + ⟩}^{\otimes n} - {| - ⟩}^{\otimes n})

3-

| \pm ⟩ = \frac{1}{\sqrt{2}} (| 0 ⟩ \pm | 1 ⟩)

4-

{| + ⟩, | - ⟩}

5-

{| 0 ⟩, | 1 ⟩}

6-

| Ψ^{n} ⟩ = a | 0^{n} ⟩ + b | 1^{n} ⟩

7-

| Ψ^{n - 1} ⟩

8-

a | 1^{n - 1} ⟩ + b | 0^{n - 1} ⟩

9-

| Ψ^{n - 1} ⟩

10-

(n + m - 1)

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0703322

Formulas:

1-

r a d i u s <

2-

r a d i u s >

3-

M_{B, t o t}

4-

[α / F e]

5-

χ^{2} / D O F = 1.6

6-

{(M / L)}_{*, B} = 19 \pm 2 {(M / L)}_{⊙}

7-

(1.7 \pm 0.4) \cdot 10^{10} M_{⊙}

8-

μ_{B e} = 19.60

9-

[Fe/H] = - 0.2

10-

M_{B} = - 18.9, - 18.6

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/math/0508081

Formulas:

1-

P G (2, q)

2-

x^{T} y = 0

3-

E R (q)

4-

P G (2, q)

5-

E R (q)

6-

q^{2} + q + 1

7-

E R (q)

8-

b_{j, i} = b_{i, j}

9-

E R (q)

10-

P G (2, q)

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/0911.5530

Formulas:

1-

F_{H} = \int \int [\frac{k_{c}}{2} {(2 H + C_{0})}^{2} + \bar{k} Λ] 𝑑 A

2-

F_{S} = λ \oint 𝑑 A

3-

F_{V} = Δ P \oint 𝑑 V

4-

F = F_{H} + F_{S} + F_{V}

5-

δ^{(1)} F = 0

6-

k_{c} (2 H + C_{0}) (2 H^{2} - 2 Λ - C_{0} H)

7-

- 2 λ H + 2 k_{c} \nabla^{2} H + Δ P

8-

ℱ = ℱ (H, Λ)

9-

\tan ψ (x) = \frac{d z}{d x}

10-

H = \frac{1}{2} \cos ψ \frac{d ψ}{d x} = \frac{1}{2} \frac{d (\sin ψ)}{d x}, Λ = 0 .

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/astro-ph/0312365

Formulas:

1-

τ_{350 μ m} \sim 1.5

2-

P \geq 3 σ_{P}

3-

P \geq 2 σ_{P}

4-

P + 2 σ_{P} < 1 %

5-

P \geq 2 σ_{P}

6-

P + 2 σ_{P} < 1 %

7-

Δ α ≃ - 3'

8-

Δ δ ≃ 17'

9-

Δ α ≃ 3'

10-

Δ δ ≃ 14.4'

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/2011.13693

Formulas:

1-

σ_{i n - p l a n e}

2-

(c m^{- 1})

3-

(c m^{- 1} / G P a)

4-

(c m^{- 1} / G P a)

5-

σ_{x y} = σ_{x z} = σ_{y z} = 0

6-

σ_{i n - p l a n e} = σ_{x x} = σ_{y y}

7-

σ_{x x, y y, z z}

8-

Δ w_{i} = w_{i} - w_{0 i};

9-

Δ w_{i} = 2 a_{i}^{'} σ_{i n - p l a n e} + b_{i}^{'} σ_{z z};

10-

Δ w_{j} = 2 a_{j}^{'} σ_{i n - p l a n e} + b_{j}^{'} σ_{z z};

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/0903.0288

Formulas:

1-

E_{b i n} = E_{H_{2}} - 2 E_{H} = - 4.55

2-

[\bar{2} 11]

3-

[\bar{1} \bar{1} 2]

4-

U (x, y, z) = A (x, y) {1 - e^{- B (x, y) [z - C (x, y)]}}^{2} + D (x, y),

5-

[\bar{1} 10]

6-

[\bar{1} \bar{1} 2]

7-

E_{a d s}

8-

E_{v i b}^{⟂}

9-

E_{v i b}^{∥}

10-

[h k l]

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1707.05749

Formulas:

1-

𝐏 + (1 / 2) 𝐄

2-

𝐅_{⊥}^{E} = 𝐃 - 𝐆

3-

| 𝐐𝐆 | = E \sin α

4-

β \in [- π / 2, π / 2]

5-

| 𝐅_{⊥}^{E} | = | 𝐃𝐆 | = E \sin α \sin β .

6-

| 𝐯_{⊥} | / | 𝐯 | = v_{⊥} / v

7-

| 𝐅_{⊥}^{B} | = \frac{v}{c} \frac{v_{⊥}}{v} B = \frac{v}{c} B \frac{\sin α \cos β}{\sqrt{\cos^{2} α + \sin^{2} α \cos^{2} β}} .

8-

u = \sin^{2} β

9-

u^{2} \sin^{2} α - u (k + 1) + k = 0,

10-

k = (v^{2} / c^{2}) (B^{2} / E^{2})

Formulas (html):

Correct Categorie: physics

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/physics/0506013

Formulas:

1-

\prod s_{i j}^{n_{i j}}

2-

\prod s_{i j}^{n_{i j}}

3-

ℒ = \frac{1}{2} ϕ ϕ + \frac{1}{2} m^{2} ϕ^{2} + \frac{1}{3!} λ_{3} ϕ^{3}

4-

ℒ_{bare} = \frac{1}{4!} ϕ^{4} + \sum 𝒪_{i} .

5-

ϕ^{2} ϕ^{2}

6-

A_{s_{i j}} = f_{s_{i j}, n_{i j}} \prod s_{i j}^{n_{i j}},

7-

s_{i j} = (k_{i} + k_{j})

8-

f_{s_{i j}, n_{i j}}

9-

f_{s_{i j}, n_{i j}}

10-

f_{s_{i j}, n_{i j}}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/math/9706218

Formulas:

1-

π_{1} (M)

2-

π_{1} (M)

3-

π_{1} (M)

4-

p : \tilde{M} \to M

5-

π_{1} (F)

6-

N (H) = {g \in π_{1} (M) | g H g^{- 1} = H}

7-

A u t (p) ≅ N (H) / H

8-

π_{1} (M)

9-

p : \tilde{M} \to M

10-

p_{*} (π_{1} (\tilde{M})) = H

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/astro-ph/9810489

Formulas:

1-

m_{I} (A B) < 23.0

2-

z_{p h o t o} > 0.7

3-

z_{p h o t o}

4-

m_{I} (A B) \leq 23.0

5-

z_{p h o t o} > 0.7

6-

R \equiv λ / Δ λ = 3700

7-

m_{I} (A B) \leq 23.0

8-

z_{p h o t o} > 0.7

9-

500 \times 60 \times 8 h^{- 3}

10-

ξ (r_{p}, π)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1806.00418

Formulas:

1-

(T E_{m})

2-

n (x, z)

3-

{\nabla^{2} + {[k_{0} n (x, z)]}^{2}} E_{y} (x, z) = 0

4-

k_{0} = 2 π / λ_{0}

5-

E_{y} (x, z) = \sum_{m} a_{m} (z) e_{m} (x, z) \exp [i \int_{0}^{z} β_{m} (z) 𝑑 z],

6-

a_{m} (z)

7-

e_{m} (x, z)

8-

β_{m} (z)

9-

ℋ e_{m} (x) = β_{m}^{2} e_{m} (x)

10-

ℋ = d^{2} / d x^{2} + {[k_{0} n (x)]}^{2}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: cond-mat

Result: incorrect

Run 6831306 (Agent374)