Run 6969985

Paper: https://arxiv.org/abs/cond-mat/0407704

Formulas:

1-

H = - \frac{ℏ^{2}}{2 m} \nabla^{2} + V (𝐫, 𝝈) + e E x + V_{i} (𝐫, 𝝈)

2-

𝒥 (𝐫) = \sum_{𝐤 λ} G_{𝐤 λ} f (ϵ_{𝐤 λ}, 𝐫)

3-

G_{𝐤 λ} = \int 𝑑 𝐫 Ψ_{𝐤 λ}^{+} (𝐫) \hat{𝐆} 𝚿_{𝐤 λ} (𝐫) \equiv < 𝚿_{𝐤 λ} | \hat{𝐆} | 𝚿_{𝐤 λ} >

4-

Ψ_{𝐤 λ} (𝐫)

5-

f (ϵ_{𝐤 λ}, 𝐫)

6-

V_{i} (𝐫, σ)

7-

Ψ_{𝐤 λ} (𝐫) = Ψ_{𝐤 λ}^{(0)} (𝐫) + Ψ_{𝐤 λ}^{(1)} (𝐫)

8-

Ψ_{𝐤 λ}^{(0)} (𝐫)

9-

Ψ_{𝐤 λ}^{(1)} (𝐫) = \sum_{𝐤^{'} λ^{'} \neq 𝐤 λ} \frac{< Ψ_{𝐤^{'} λ^{'}}^{(0)} | e E x | Ψ_{𝐤 λ}^{(0)} >}{ϵ_{𝐤 λ} - ϵ_{𝐤^{'} λ^{'}}} Ψ_{𝐤^{'} λ^{'}}^{(0)} (𝐫),

10-

f (ϵ_{𝐤 λ}, 𝐫) = f^{0} (ϵ_{𝐤 λ}) + (- \frac{\partial f^{0}}{\partial ϵ_{𝐤 λ}}) g (𝐤 λ, 𝐫)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/hep-ph/9812206

Formulas:

1-

2 | p_{L} | / \sqrt{s} ≲ 0.005

2-

c < p_{T} < 1

3-

q + \bar{q} \to γ + g

4-

g + q (\bar{q}) \to γ + q (\bar{q})

5-

k (M_{G}^{2}) \frac{t_{0}}{V_{0}} \sum_{i = 2}^{N_{p}} \sum_{j < i} \int {[{(p_{i} \cdot p_{j})}^{2} - m_{i}^{2} m_{j}^{2}]}^{1 / 2}

6-

\frac{σ_{i j} (s_{i j})}{E_{i} E_{j}} δ (\sum_{k = 1}^{N_{p}} E_{k} - M) δ (\sum_{k = 1}^{N_{p}} 𝐩_{k}) \prod_{k = 1}^{N_{p}} \frac{d^{3} p_{k}}{E_{k}},

7-

σ_{i j} (s_{i j})

8-

q + \bar{q} \to γ + g

9-

g + q (\bar{q}) \to γ + q (\bar{q})

10-

{[k (M_{G}^{2})]}^{- 1} = \int δ (\sum_{k = 1}^{N_{p}} E_{k} - M) δ (\sum_{k = 1}^{N_{p}} 𝐩_{k}) \prod_{k = 1}^{N_{p}} \frac{d^{3} p_{k}}{E_{k}} .

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/9710056

Formulas:

1-

L i N b O_{3}

2-

ω = 2 π f

3-

< 10^{- 7} W

4-

n = 6.7 \cdot 10^{11} c m^{- 2}

5-

μ = 1.28 \cdot 10^{5} c m^{2} / V s

6-

n = 7 \cdot 10^{11} c m^{- 2}

7-

σ_{x x} (B)

8-

Γ (σ_{x x})

9-

σ_{X X}^{A C}

10-

σ_{X X}^{D C}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cs

Result: incorrect

Paper: https://arxiv.org/abs/physics/9611013

Formulas:

1-

Δ μ^{e x} = - k T \ln p_{0} .

2-

p_{n} = \exp (λ_{0} + λ_{1} n + λ_{2} n^{2})

3-

⟨ n (n - 1) ⟩

4-

ρ^{2} \int_{v} 𝑑 𝐫 \int_{v} 𝑑 𝐫^{'} g (| 𝐫 - 𝐫^{'} |) .

5-

Δ μ^{e x}

6-

Δ μ^{e x}

7-

Δ μ^{e x} \approx T ρ^{2} {k v^{2} / 2 σ^{2}} + T {k \ln (2 π σ^{2}) / 2} .

8-

\exp (- δ n^{2} / 2 σ^{2}) / \sqrt{2 π σ^{2}}

9-

δ n = n - ⟨ n ⟩

10-

σ^{2} = ⟨ δ n^{2} ⟩

Formulas (html):

Correct Categorie: physics

Guessed Categorie: cs

Result: incorrect

Paper: https://arxiv.org/abs/math/0109106

Formulas:

1-

\bar{f} : X \to L

2-

X τ L^{'}

3-

ext - \dim (X) \leq [L]

4-

ext - \dim (X) \leq [L]

5-

ext - \dim (X) \leq [L]

6-

i_{0} = \min {i : π_{i} (L) \neq 0}

7-

ext - \dim (S^{i_{0}}) \leq [L]

8-

x y = x z

9-

x, y, z \in S

10-

ext - \dim (X) \leq [L]

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/hep-ph/0606233

Formulas:

1-

Y = \log (s)

2-

T (r, Y)

3-

T (r, Y)

4-

r Q_{s} (Y)

5-

Q_{s} (Y)

6-

T (r, Y_{0})

7-

T (r, Y) = T (\log [r^{2} {\bar{Q}}_{s}^{2} (Y)] / \sqrt{Y})

8-

⟨ T^{(k)} ⟩

9-

(𝐱_{1}, 𝐲_{1}), \dots, (𝐱_{k}, 𝐲_{k})

10-

⟨ T^{(k)} ⟩

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/1503.04635

Formulas:

1-

m i c r o s c o p i c

2-

m o d e l . -

3-

H_{S} = (p_{S}^{2} + ω_{S}^{2} q_{S}^{2}) / 2

4-

H_{E} = \sum_{i = 1}^{N} (P_{i}^{2} + Ω_{i}^{2} Q_{i}^{2}) / 2

5-

H_{I} = q_{S} \sum_{i = 1}^{N} g_{i} Q_{i}

6-

H = H_{S} + H_{E} + k H_{I}

7-

γ (t) = \sum_{i = 1}^{N} (k^{2} g_{i}^{2} / Ω_{i}^{2}) \cos (Ω_{i} t)

8-

J (ω) = \frac{π}{2} \sum_{i} \frac{k^{2} g_{i}^{2}}{Ω_{i}} δ (ω - Ω_{i})

9-

J (ω) = ω \int_{0}^{\infty} γ (t) \cos (ω t) 𝑑 t .

10-

E n g i n e e r i n g

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/1504.01059

Formulas:

1-

| A | = {| G |}^{α}

2-

| A | = {| G |}^{α}

3-

\hat{1_{A}} (γ) = \sum_{x \in A} γ (x) .

4-

{Spec}_{ε} (A) = {γ \in \hat{G} : | \hat{1_{A}} (γ) | \geq ε | A |} .

5-

{Spec}_{ε} (A) = - {Spec}_{ε} (A)

6-

| A | \geq {| G |}^{c}

7-

| A | = {| G |}^{α}

8-

α > 0, ε > 0

9-

| {Spec}_{ε} (A) | \leq \frac{| G |}{ε^{2} | A |} = \frac{{| G |}^{1 - α}}{ε^{2}} .

10-

γ_{1}, \dots, γ_{d} \in \hat{G}

Formulas (html):

Correct Categorie: math

Guessed Categorie: q-bio

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0310550

Formulas:

1-

i ℏ \frac{\partial ψ}{\partial t} = - \frac{ℏ^{2}}{2 m} Δ ψ + V_{e x t} (𝐫) ψ + g {| ψ |}^{2} ψ,

2-

V_{e x t} (𝐫) = \frac{1}{2} m (ω_{x}^{2} x^{2} + ω_{y}^{2} y^{2} + ω_{z}^{2} z^{2})

3-

g = 4 π ℏ^{2} a_{s} / m

4-

\int {| ψ |}^{2} 𝑑 𝐫 = N .

5-

S = \int L 𝑑 t, L = \int ℒ 𝑑 𝐫,

6-

ℒ = \frac{i ℏ}{2} (ψ_{t}^{*} ψ - ψ_{t} ψ^{*}) + \frac{ℏ^{2}}{2 m} {| \nabla ψ |}^{2} + V_{e x t} {| ψ |}^{2} + \frac{1}{2} g {| ψ |}^{4},

7-

λ = \frac{ω_{z}}{ω_{⊥}} ≪ 1,

8-

a_{⊥} = {(ℏ / m ω_{⊥})}^{1 / 2}

9-

N \sim {| ψ |}^{2} a_{⊥}^{2} Z_{0}

10-

\frac{N a_{s}}{Z_{0}} ≪ 1 .

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1404.4668

Formulas:

1-

λ_{SPP} / λ_{0} ≃ 2 α E_{F} / (ϵ ℏ ω) \sim α

2-

ℏ ω < 2 E_{F}

3-

k_{SPP} = \frac{2 π h^{2} c^{2} ϵ_{0} κ}{e^{2} E_{F} λ_{0}^{2}},

4-

κ = κ_{1} + i κ_{2} = (ϵ_{1} + ϵ_{2}) / 2

5-

r \propto 1 / k_{tip}

6-

E_{ref} / E_{bg} \geq 10

7-

\tilde{A} = A e^{i Φ}

8-

A = | \tilde{A} |

9-

ϕ = Arg (\tilde{A})

10-

A = | \tilde{A} |

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1101.0119

Formulas:

1-

0 ν β β

2-

0 ν β β

3-

0 ν β β

4-

0 ν β β

5-

0 ν β β

6-

0 ν β β

7-

(n, n^{'} γ)

8-

0 ν β β

9-

(n, n^{'} γ)

10-

0 ν β β

Formulas (html):

Correct Categorie: nucl-ex

Guessed Categorie: q-fin

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0511593

Formulas:

1-

0.24 \leq z_{lens} \leq 0.5

2-

\sim 500 h^{- 1}

3-

σ ≳ 300 km s^{- 1}

4-

E (B V) \leq 0.2

5-

\sim 36' \times 36'

6-

r_{vir} \approx 500 h^{- 1} kpc \sim 3'

7-

0.35 \leq z_{lens} \leq 0.5

8-

= 1 \overset{''}{.} 3

9-

V + a_{0} + a_{1} (V - I) + a_{2} (X - 1.25)

10-

R + b_{0} + b_{1} (R - I) + b_{2} (X - 1.25)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/1510.05932

Formulas:

1-

Rm = Ω_{i} r_{i}^{2} / η

2-

S = B_{0} r_{i} / η \sqrt{μ ρ}

3-

Rm \sim O (10)

4-

Pm = η / ν \sim O (10^{- 6})

5-

Re \sim O (10^{7})

6-

B_{ϕ} = 1 / r

7-

Re \sim O (10^{3})

8-

B_{ϕ} = 1 / r

9-

r_{i} / r_{o} = 0.5

10-

𝐔_{𝟎} = (0, r Ω 𝐞_{ϕ}, 0)

Formulas (html):

Correct Categorie: physics

Guessed Categorie: q-bio

Result: incorrect

Paper: https://arxiv.org/abs/hep-ph/0206245

Formulas:

1-

ϵ^{2} \approx \frac{{(1 + \tan^{2} θ_{atm})}^{3}}{| \tan^{2} θ_{sun} - \cot^{2} θ_{sun} |} \cdot \frac{Δ m_{sun}^{2}}{Δ m_{atm}^{2}},

2-

(Δ m_{sun}^{2}, Δ m_{atm}^{2})

3-

(θ_{sun}, θ_{atm})

4-

(3.3 - 17) \times 10^{- 5} {eV}^{2},

5-

Δ m_{sun}^{2} = (5 - 7) \times 10^{- 5} {eV}^{2}

6-

\tan^{2} θ_{sun} = 0.35 - 0.45

7-

(1.6 - 3.9) \times 10^{- 3} {eV}^{2},

8-

\sin^{2} 2 θ_{atm}

9-

ϵ \approx \sqrt{m_{u} / m_{c}} \approx 0.04 - 0.08

10-

SU {(2)}_{L} \times U {(1)}_{Y}

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: eess

Result: incorrect

Paper: https://arxiv.org/abs/hep-th/0104084

Formulas:

1-

E_{d} \sim Q_{d}^{(d / d + 1)}

2-

E \sim Q^{(3 / 4)}

3-

Q^{(3 / 4)}

4-

E_{d} \sim Q_{d}^{d / (d + 1)}

5-

ℒ = \int d^{d} x (\frac{1}{2} \partial_{μ} ϕ_{a} \partial^{μ} ϕ_{a} - V (| ϕ |))

6-

| ϕ | = \sqrt{ϕ_{1}^{2} + ϕ_{2}^{2}}

7-

S O (2)

8-

Q = \int d^{d} x ϵ_{a b} ϕ_{a} \partial_{t} ϕ_{b} .

9-

V (| ϕ |) = {\begin{matrix} \frac{1}{2} m^{2} {| ϕ |}^{2} & | ϕ | \to 0 \\ Λ & | ϕ | \to \infty \end{matrix}

10-

ϕ_{1} + i ϕ_{2} = e^{i ω t} φ (r)

Formulas (html):

Correct Categorie: hep-th

Guessed Categorie: hep-th

Result: correct

Paper: https://arxiv.org/abs/1102.1580

Formulas:

1-

{1, 2, \dots, k}

2-

(r_{1}^{t}, \dots, r_{k}^{t})

3-

I_{t} \in {1, \dots, k}

4-

γ \in [0; 1]

5-

η \in (O; \frac{1}{k}]

6-

{1, \dots, k}

7-

t = 1, 2, \dots

8-

G_{I_{t}} = G_{I_{t}} + \frac{r_{I_{t}}^{t}}{p_{I_{t}}^{t}}

9-

i \in {1, \dots, k}

10-

p_{i}^{t + 1} = (1 - γ) \frac{\exp (η G_{i})}{\sum_{j = 1}^{k} \exp (η G_{j})} + γ

Formulas (html):

Correct Categorie: cs

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/0812.1897

Formulas:

1-

J (F) = α F + β

2-

J = E_{T} - E_{S},

3-

r = R_{y} / R_{x}

4-

R_{x} (R_{y})

5-

U_{μ} (𝐫) = - U_{0 μ} e^{- {[{(x - x_{0 μ})}^{2} / R_{μ x}^{2} + {(y - y_{0 μ})}^{2} / R_{μ y}^{2}]}^{p / 2}},

6-

U_{0 μ} > 0

7-

𝐫 = (x, y)

8-

𝐫_{0 μ} = (x_{0 μ}, y_{0 μ})

9-

R_{l x} = R_{l y} = 20

10-

R_{r x} = 20

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1009.4660

Formulas:

1-

\sim 1 m m

2-

ϕ = d_{x} d_{y} / (s_{x} s_{y})

3-

s_{x} = s_{y} = 60

4-

θ_{W} = 180^{\circ} - θ_{eq, wall}

5-

n = n_{A} + n_{B}

6-

φ = n_{A} - n_{B}

7-

\int_{V} (ψ_{b} + \frac{κ}{2} {(\partial_{α} φ)}^{2}) 𝑑 V - \int_{S} h \cdot φ 𝑑 S

8-

\frac{c^{2}}{3} n \ln n + A (- \frac{1}{2} φ^{2} + \frac{1}{4} φ^{4})

9-

γ = \sqrt{8 κ A / 9}

10-

\sqrt{2 κ A} \cdot sign (\frac{π}{2} - θ_{eq}) \cdot \sqrt{\cos (\frac{α}{3}) [1 - \cos (\frac{α}{3})]},

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: q-fin

Result: incorrect

Paper: https://arxiv.org/abs/gr-qc/9909018

Formulas:

1-

κ = 16 π G

2-

\frac{1}{κ} \int_{Ω^{-}} d^{4} x \sqrt{- g} ℛ

3-

+ \frac{2}{κ} \int_{Σ} d^{3} x \sqrt{h} {[𝒦]}_{-}^{+} - \int_{Σ} d^{3} x \sqrt{h} ρ

4-

+ \frac{1}{κ} \int_{Ω^{+}} d^{4} x \sqrt{- g} ℛ + \int_{Ω^{+}} d^{4} x \sqrt{- g} ℒ_{r a d},

5-

ℒ_{r a d}

6-

(r, θ, ϕ)

7-

4 π r^{2}

8-

θ \in (0, π)

9-

ϕ \in (0, 2 π)

10-

Ω_{i n} = Ω^{-}

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: eess

Result: incorrect

Paper: https://arxiv.org/abs/1005.2145

Formulas:

1-

B i_{2} S r_{2} C a C u_{2} O_{8 + δ}

2-

B i_{2} S r_{2} C a C u_{2} O_{8 + δ}

3-

B i_{2} S r_{2} C a C u_{2} O_{8 + δ}

4-

B i_{2} S r_{2} C a C u_{2} O_{8 + δ}

5-

x = 0.12, 0.14, 0.16, 0.19, 0.22

6-

ξ_{c o h} \approx 1 - 3

7-

ξ_{c o h}

8-

T_{c} = 84 K

9-

ξ_{c o h}

10-

r_{0} \approx a / x^{1 / 2}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cs

Result: incorrect

Paper: https://arxiv.org/abs/1310.1116

Formulas:

1-

{1, \dots, k}

2-

{1, \dots, k}

3-

{1, \dots, k}

4-

𝐭𝐝 (G) \leq 𝐭𝐝 (H)

5-

{𝐨𝐛𝐬}_{⊑} (𝒢_{k})

6-

{𝐨𝐛𝐬}_{\subseteq} (𝒢_{k})

7-

{𝐨𝐛𝐬}_{\leq} (𝒢_{k})

8-

{𝐨𝐛𝐬}_{\leq} (𝒢_{k})

9-

k \in {1, 2, 3}

10-

𝖱 \in {⊑, \subseteq, \geq}

Formulas (html):

Correct Categorie: math

Guessed Categorie: q-bio

Result: incorrect

Paper: https://arxiv.org/abs/1706.07316

Formulas:

1-

J = β \sum_{k = 1}^{N} {(θ_{o, k} - θ_{m, k})}^{2} + γ O

2-

σ_{θ} = 2 °

3-

C_{v e c}

4-

σ_{θ} = 0.0 °

5-

σ_{θ} = 2.0 °

6-

σ_{θ} = 5.0 °

7-

σ_{θ} = 10.0 °

8-

σ_{θ} = 15.0 °

9-

σ_{θ} = 20.0 °

10-

σ_{r} = 0.0 °

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: cs

Result: incorrect

Paper: https://arxiv.org/abs/1209.4912

Formulas:

1-

{(e^{π / s_{0}})}^{n} a_{-}

2-

e^{π / s_{0}} \approx 22.694

3-

a_{-} = - 21.306 a_{*} .

4-

{(e^{π / s_{0}})}^{n} a_{+}

5-

e^{- π / 2 s_{0}} a_{+} = 0.93882 a_{*}

6-

a_{+} = 4.4724 a_{*} .

7-

a_{+} / a_{-} = - e^{- π / 2 s_{0}}

8-

E_{d} = \frac{ℏ^{2}}{m a^{2}} .

9-

σ_{A A} = \frac{8 π a^{2}}{1 + a^{2} k_{cm}^{2}} .

10-

k = 2 / (\sqrt{3} a)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cs

Result: incorrect

Paper: https://arxiv.org/abs/1511.08942

Formulas:

1-

>> q^{\frac{d + 2}{3}}

2-

>> q^{\frac{d + 2}{2}}

3-

(a, b, c)

4-

(x, y, z) \in 𝔽_{q}^{d} \times 𝔽_{q}^{d} \times 𝔽_{q}^{d}

5-

A, B \subset 𝔽_{q}^{d}

6-

{| A |}^{2} | B | >> q^{d + 2}

7-

(x, y, z)

8-

| A | >> q^{\frac{d + 2}{3}}

9-

| A | ≫ q^{\frac{d + 2}{2}}

10-

| B | ≫ \frac{1}{\log q} q^{\frac{d + 2}{2}}

Formulas (html):

Correct Categorie: math

Guessed Categorie: hep-th

Result: incorrect

Paper: https://arxiv.org/abs/1104.4307

Formulas:

1-

Δ λ = - 0.048

2-

Δ λ = \pm 0.892

3-

Δ λ = \pm 1.715

4-

Δ λ = \pm 2.717

5-

B_{λ} (T_{b}) = I_{λ}^{obs}

6-

Δ λ = \pm 2.2

7-

+ 480 m Å

8-

Δ λ = - 0.048

9-

Δ T_{b} = \pm 400

10-

Δ λ = - 3

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: q-fin

Result: incorrect

Paper: https://arxiv.org/abs/1301.4264

Formulas:

1-

\bar{M_{K}} \sim - 7

2-

2 \overset{<}{\sim} M_{⊙} \overset{<}{\sim} 3

3-

\bar{M_{K}} \sim - 2

4-

\overset{<}{\sim} 2 M_{⊙}

5-

(u - g) < 0.875 (g - r) + 0.5

6-

(u - g) <

7-

(u - g) < 2 (g - r) + 0.3 \cup

8-

(u - g) > 0.9

9-

(g - r) < 0.8

10-

| b | > 30 \deg

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/1811.01797

Formulas:

1-

ℒ_{S Y M} = \frac{1}{4} F_{μ ν} F^{μ ν} + \frac{1}{2} \bar{λ} (D̸ + m_{g}) λ .

2-

N_{c} \oplus {\bar{N}}_{c}

3-

ℒ_{S Q C D} =

4-

ℒ_{S Y M} + {| D_{μ} Φ_{1} |}^{2} + {| D_{μ} Φ_{2}^{†} |}^{2} + \bar{ψ} (γ_{μ} D_{f}^{μ} + m) ψ + m^{2} {| Φ_{1} |}^{2} + m^{2} {| Φ_{2} |}^{2}

5-

+ i \sqrt{2} g {\bar{λ}}^{a} (Φ_{1}^{†} P_{+} + Φ_{2} P_{-}) T^{a} ψ - i \sqrt{2} g \bar{ψ} T^{a} (P_{-} Φ_{1} + P_{+} Φ_{2}^{†}) λ^{a}

6-

+ \frac{g^{2}}{2} {(Φ_{1}^{†} T^{a} Φ_{1} - Φ_{2} T^{a} Φ_{2}^{†})}^{2} .

7-

SU (N_{c})

8-

\frac{3}{2} N_{c} < N_{f} < 3 N_{c}

9-

SU (N_{c})

10-

SU (N_{c} - N_{f})

Formulas (html):

Correct Categorie: hep-lat

Guessed Categorie: cs

Result: incorrect

Paper: https://arxiv.org/abs/hep-ph/0008010

Formulas:

1-

- ℒ_{m a s s} = {\bar{l}}_{i L} {(M_{l})}_{i j} l_{j R} + {\bar{ν}}_{i L} {(M_{D})}_{i j} ν_{j R} + \frac{1}{2} ν_{i R}^{T} C {(M_{R})}_{i j} ν_{j R} + h . c .,

2-

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

3-

M_{k} = c_{k} [Δ + P_{k}],

4-

Δ = (\begin{matrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{matrix}), P_{k} = (\begin{matrix} 0 & 0 & 0 \\ 0 & a_{k} & 0 \\ 0 & 0 & b_{k} \end{matrix}), k = l, D, R

5-

| a_{k} |, | b_{k} | ≪ 1

6-

{(a, b, c)}_{D}

7-

M_{eff} = - M_{D} M_{R}^{- 1} M_{D}^{T} = - c_{eff} [Δ + P_{D}] Z {[Δ + P_{D}]}^{T},

8-

c_{eff} = c_{D}^{2} / c_{R}

9-

Z \equiv {[Δ + P_{R}]}^{- 1} = \frac{1}{a_{R} b_{R}} . (\begin{matrix} a_{R} + b_{R} + a_{R} b_{R} & - b_{R} & - a_{R} \\ - b_{R} & b_{R} & 0 \\ - a_{R} & 0 & a_{R} \end{matrix}) .

10-

M_{0} \equiv - M_{eff} / c_{eff}

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: cs

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0402430

Formulas:

1-

t, ϕ, r, θ

2-

d s^{2} = (β^{2} - α^{2}) d p t^{2} + 2 β_{i} d x^{i} d t + γ_{i j} d x^{i} d x^{j},

3-

γ_{i j} = (\begin{matrix} Σ \sin^{2} θ / κ^{2} & - a \sin^{2} θ (1 + Z) & 0 \\ - a \sin^{2} θ (1 + Z) & 1 + Z & 0 \\ 0 & 0 & κ^{2} \end{matrix}),

4-

α = 1 / \sqrt{1 + Z},

5-

β^{i} = (0, \frac{Z}{1 + Z}, 0) .

6-

r^{2} + a^{2} \cos^{2} θ,

7-

2 r / κ^{2},

8-

{(r^{2} + a^{2})}^{2} - a^{2} Δ \sin^{2} θ,

9-

r^{2} + a^{2} - 2 r .

10-

G = M = c = 1

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: q-bio

Result: incorrect

Paper: https://arxiv.org/abs/1510.02554

Formulas:

1-

K = K_{0}, K_{1}, \dots, K_{n}

2-

(i = 1, 2, \dots, n)

3-

K = K_{0}, K_{1}, \dots, K_{n}

4-

(i = 1, 2, \dots, n)

5-

D = D_{0}, D_{1}, \dots, D_{n} = D^{'}

6-

(i = 1, 2, \dots, n)

7-

G = G (D)

8-

G (D) = G (D^{'})

9-

c (K) \geq 3

10-

u (K) \leq \frac{c (K) - 1}{2}

Formulas (html):

Correct Categorie: math

Guessed Categorie: q-bio

Result: incorrect

Paper: https://arxiv.org/abs/1806.09214

Formulas:

1-

𝑭 (x, y, z) = \frac{2 α I_{a c} (x, y, z)}{c} 𝒆_{p},

2-

I_{a c} = I_{0} I (x, y, z)

3-

I (x, y, z)

4-

I_{0} = P_{a c} / (π R_{t}^{2} / 4)

5-

𝑭 (x, y, z) = [\frac{2 α P_{a c}}{c π R_{t}^{2}}] 4 I (x, y, z) 𝒆_{p} .

6-

ρ ν^{2} / H^{2}

7-

\nabla \cdot 𝒖 = 0,

8-

\frac{\partial 𝒖}{\partial t} + (𝒖 \cdot \nabla) 𝒖 = - \nabla p + \nabla^{2} 𝒖 + A^{*} 4 I (x, y, z) 𝒆_{p},

9-

A^{*} = \frac{2 α P_{a c} H^{3}}{c π R_{t}^{2} ρ ν^{2}} .

10-

A = 10^{- 6} A^{*}

Formulas (html):

Correct Categorie: physics

Guessed Categorie: cs

Result: incorrect

Paper: https://arxiv.org/abs/1108.6231

Formulas:

1-

A l_{x} G a_{1 - x} A s

2-

S = d L / d I

3-

A l_{0.5} G a_{0.5} A s

4-

A l_{0.33} G a_{0.67} A s

5-

A l_{0.08} G a_{0.92} A s

6-

A l_{0.33} G a_{0.67} A s

7-

A l_{0.5} G a_{0.5} A s

8-

r = d U / d I

9-

S_{0} = d L / d I

10-

A l_{0.5} G a_{0.5} A s

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cs

Result: incorrect

Paper: https://arxiv.org/abs/1811.03368

Formulas:

1-

m_{A} = M - E, m_{B} = M - d m, m_{C} = m_{0}, m_{D} = M .

2-

f_{A} f_{B} = f_{C} f_{D}, f_{i} = 1 - 2 m_{i} / R, i = A, B, C, D .

3-

ξ = R / (2 M) - 1, α = d m / M, β = m_{0} / M, η = E / M,

4-

η = (1 - α - β) ξ / (α + ξ) .

5-

0 < ξ ≪ α ≪ 1

6-

η \sim ξ / α ≪ 1

7-

ξ = ξ_{0} \exp (- t / (2 M))

8-

ξ = ξ_{0} \exp (- τ / (4 M)) .

9-

τ = - 4 M (\log ξ - \log ξ_{0})

10-

0 < ξ, α ≪ 1

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: q-bio

Result: incorrect

Paper: https://arxiv.org/abs/1212.2176

Formulas:

1-

d B_{i} = - \sum_{j = 1, j \neq i}^{n} \frac{[B_{i}, B_{j}]}{a_{i} - a_{j}} d (a_{i} - a_{j}), i = 1, \dots, n,

2-

i = 1, \dots, n

3-

a = (a_{1}, \dots, a_{n})

4-

[B_{i}, B_{j}]

5-

B_{i} (a)

6-

{a | a = (a_{1}, \dots, a_{n}) \in {\bar{ℂ}}^{n} ∖ ⋃_{i, j} A_{i j}}, A_{i j} = {a | a_{i} = a_{j}} .

7-

Ω = ⋃_{i, j} A_{i j} .

8-

a^{0} = (a_{1}^{0}, \dots, a_{n}^{0})

9-

a^{0} \in Ω^{'} = Ω ∖ (⋃_{i, j, k} A_{i j k}), A_{i j k} = {a | a_{i} = a_{j} = a_{k}} .

10-

(a_{s} - a_{r})

Formulas (html):

Correct Categorie: math

Guessed Categorie: q-bio

Result: incorrect

Paper: https://arxiv.org/abs/1305.4208

Formulas:

1-

m_{H}^{2} + m_{W}^{2} + m_{Z}^{2} + \sum_{f = q, l} m_{f}^{2} = v^{2},

2-

m_{H} = (125.6 \pm 0.4)

3-

m_{t} = (173.5 \pm 0.9)

4-

v^{2} = 1 / (\sqrt{2} G_{F}) = {(246.2 GeV)}^{2}

5-

2 λ + \frac{g^{2}}{4} + \frac{g^{2} + g^{', 2}}{4} + \sum_{f} \frac{y_{f}^{2}}{2} = 1,

6-

λ, g, g^{'}

7-

V (Φ) = λ {(Φ^{†} Φ - v^{2} / 2)}^{2},

8-

m_{H}^{2} = 2 λ v^{2}

9-

v^{2} = 1 / (\sqrt{2} G_{F})

10-

m_{H} = (124.5 \pm 0.8)

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: cs

Result: incorrect

Paper: https://arxiv.org/abs/1005.3926

Formulas:

1-

R_{k} (L)

2-

R_{k} (C_{n}) = 2^{k - 1} (n - 1) + 1 for n > 3 .

3-

R_{k} (C_{n}) \leq (k + 2)! n

4-

R_{k} (C_{n}) \leq k 2^{k} n + o (n), as n \to \infty .

5-

R_{k} (C_{n}) \geq (k - 1) n - 2 k + 4 .

6-

R_{k} (C_{n}) \leq k n + o (n), as n \to \infty .

7-

G = (V, E)

8-

L_{1}, \dots, L_{k}

9-

R (L_{1}, \dots, L_{k})

10-

L_{1} = L_{2} = \dots = L_{k} = L

Formulas (html):

Correct Categorie: math

Guessed Categorie: cs

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0507515

Formulas:

1-

R_{1} \sim ω^{- 0.5}

2-

\frac{M_{0} - M (τ)}{M_{0}}

3-

A_{fast} e^{- τ / T_{1}^{f}} + A_{slow} e^{- τ / T_{1}^{s}}

4-

\frac{M_{0} - M (τ)}{M_{0}}

5-

A_{slow} e^{- τ / T_{1}^{s}} .

6-

T_{1}^{f} > 10^{4}

7-

T_{1}^{- 1} \propto ω^{- 0.5}

8-

\frac{τ_{c}}{1 + {(ω τ_{c})}^{2}}

9-

\frac{1}{ω^{2} τ_{c}} (if ω τ_{c} ≫ 1) .

10-

ω τ_{c} ≫ 1

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: q-bio

Result: incorrect

Paper: https://arxiv.org/abs/1603.07596

Formulas:

1-

Δ m (0 \overset{''}{.} 15)

2-

Δ m (1^{''})

3-

0 \overset{''}{.} 15

4-

P^{*} = {(ρ / p)}^{3 / 2} M^{- 1 / 2}

5-

Δ y = Δ I = 0.2 \pm 0.05

6-

Δ H p_{AB} = 0.69

7-

(179^{\circ}, 1 \overset{''}{.} 6)

8-

(235^{\circ}, 0 \overset{''}{.} 19)

9-

Δ y = Δ I = 0.2 \pm 0.05

10-

V = (7.35, 10.4, 10.6)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0409543

Formulas:

1-

V_{s y s} = 530

2-

V_{s y s} = 1680

3-

V_{s y s}

4-

V_{k i c k}

5-

V_{k i c k}

6-

V_{c i r c}

7-

V_{k i c k}

8-

V_{c i r c} = 0.5

9-

V_{c i r c}

10-

V_{k i c k}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: cs

Result: incorrect

Paper: https://arxiv.org/abs/1101.5827

Formulas:

1-

ℛ \equiv R_{obs} - R_{pred}

2-

R \sim 1.1 R_{Jup}

3-

R = 1.38 \pm 0.02 R_{Jup}

4-

T_{eff} = {(\frac{R_{⋆}}{2 a})}^{1 / 2} \frac{T_{⋆}}{{(1 - e^{2})}^{1 / 8}},

5-

0.1 M_{Jup} < M_{pl} < 10.0 M_{Jup}

6-

χ_{m}^{2} = \frac{1}{(N - N_{f})} \sum_{i = 1}^{N} \frac{{(R_{m_{i}} - R_{o_{i}})}^{2}}{σ_{i}^{2}},

7-

χ_{n u l l}^{2}

8-

R_{a v} = 1.2 R_{Jup}

9-

0.1 M_{Jup} < M_{pl} < 10.0 M_{Jup}

10-

χ_{n u l l}^{2} = 32.6

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: cs

Result: incorrect

Paper: https://arxiv.org/abs/math/0701733

Formulas:

1-

# (U) = # (D) = n

2-

# (U) \geq # (D)

3-

(2 n, 0)

4-

(1, - 1)

5-

𝒟 = ⋃_{n \geq 0} 𝒟_{n}

6-

| 𝒟 (n) |

7-

C_{n} = \frac{1}{n + 1} (\binom{2 n}{n})

8-

𝔏 = {ℒ_{0}, ℒ_{1}, ℒ_{2}, \dots}

9-

a_{k} = | ℒ_{k} |

10-

C \in ℒ (k)

Formulas (html):

Correct Categorie: math

Guessed Categorie: q-bio

Result: incorrect

Paper: https://arxiv.org/abs/hep-th/9312025

Formulas:

1-

i = 1, \dots, m

2-

{\bar{D}}_{\pm} U_{i} = 0

3-

p = 1, \dots, n

4-

{\bar{D}}_{+} V_{p} = D_{-} V_{p} = 0

5-

K (U_{i}, {\bar{U}}_{i}, V_{p}, {\bar{V}}_{p})

6-

S = \frac{1}{2 π α^{'}} \int d^{2} x D_{+} D_{-} {\bar{D}}_{+} {\bar{D}}_{-} K (U_{i}, {\bar{U}}_{i}, V_{p}, {\bar{V}}_{p}) .

7-

\begin{matrix} S = & - \frac{1}{2 π α^{'}} \int d^{2} x [K_{u_{i} {\bar{u}}_{j}} \partial^{a} u_{i} \partial_{a} \bar{u}_{j} - K_{v_{p} {\bar{v}}_{q}} \partial^{a} v_{p} \partial_{a} \bar{v}_{q} \\ + ϵ_{a b} (K_{u_{i} {\bar{v}}_{p}} \partial_{a} u_{i} \partial_{b} \bar{v}_{p} + K_{v_{p} {\bar{u}}_{i}} \partial_{a} v_{p} \partial_{b} \bar{u}_{i})], \end{matrix}

8-

K_{u_{i} {\bar{u}}_{j}} = \frac{\partial^{2} K}{\partial U_{i} \partial {\bar{U}}_{j}}

9-

Φ (u_{i}, v_{p})

10-

δ c = c - \frac{3 D}{2}

Formulas (html):

Correct Categorie: hep-th

Guessed Categorie: q-bio

Result: incorrect

Paper: https://arxiv.org/abs/1907.11067

Formulas:

1-

7.5 \cdot 10^{- 7} - 1 \cdot 10^{- 4}

2-

W a t t / m^{2}

3-

4 π r^{2}

4-

30 â € “ 35 %

5-

α_{M} = 0.85, α_{m} = 0.25;

6-

α (T) = \frac{α_{m} - α_{M}}{T_{2} - T_{1}} (T - T_{1}) + α_{M}

7-

P = σ A T^{4}

8-

σ = 5.67 \times 10^{- 8}

9-

W a t t s / (m^{2} K^{4})

10-

R_{i n} = \frac{F_{s} A}{4} (1 - α (T))

Formulas (html):

Correct Categorie: physics

Guessed Categorie: q-bio

Result: incorrect

Paper: https://arxiv.org/abs/hep-ph/0307176

Formulas:

1-

SU {(2)}_{L}

2-

- \frac{g}{\sqrt{2}} {\bar{u}}_{L} γ^{μ} V d_{L} W_{μ}^{+} + h . c .,

3-

- \frac{g}{2 c_{W}} ({\bar{u}}_{L} γ^{μ} X^{u} u_{L} - {\bar{d}}_{L} γ^{μ} d_{L} - 2 s_{W}^{2} J_{EM}^{μ}) Z_{μ},

4-

X^{u} = V V^{†}

5-

b \to s l^{+} l^{-}

6-

K^{+} \to π^{+} ν \bar{ν}

7-

K_{L} \to μ^{+} μ^{-}

8-

O (10^{- 1})

9-

V_{t b} = 0.999

10-

V_{t b} \geq 0.6

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-lat

Result: incorrect

Paper: https://arxiv.org/abs/1210.7802

Formulas:

1-

H_{0} = 71 km / s / Mpc, Ω_{m} = 0.27, Ω_{Λ} = 0.73

2-

\sim 50 \frac{Γ}{1 + z} MeV

3-

p^{+} + γ \to Δ^{+}

4-

Δ^{+} \to π^{+} + n

5-

Δ^{+} \to π^{0} + p^{+}

6-

π^{0} \to γ + γ

7-

ν_{p} (1 + z) / Γ

8-

γ_{p} ≳ 2 \times 10^{4} Γ_{2} ν_{p, 6}^{- 1} {(1 + z)}^{- 1},

9-

X_{n} \equiv \frac{X}{10^{n}}

10-

\sim 100 Γ_{2}^{2} ν_{p, 6}^{- 1} {(1 + z)}^{- 2}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: q-bio

Result: incorrect

Paper: https://arxiv.org/abs/1203.4109

Formulas:

1-

F d \bar{3} m

2-

(2 \times 2 \times 1)

3-

E_{DFT - D} = E_{KS - DFT} + E_{Disp}

4-

E_{Disp} = - s_{6} \sum_{i = 1}^{N - 1} \sum_{j = i + 1}^{N} \frac{C_{6}^{i j}}{R_{i j}^{6}} f_{dmp} (R_{i j})

5-

C_{6}^{i j} = \sqrt{C_{6}^{i} C_{6}^{j}}

6-

N I_{p}^{i} α^{i}

7-

f_{dmp} (R_{i j})

8-

f_{dmp} (R_{i j}) = \frac{1}{1 + e^{- d (\frac{R_{i j}}{R_{r}} - 1)}}

9-

Δ E_{ads} = E_{system (MCPM + {SiO}_{2})} - E_{molecule (MCPM, g)} - E_{clean surface ({SiO}_{2})}

10-

E_{system (MCPM + {SiO}_{2})}

Formulas (html):

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id="S2.E1.m1.1.1.3.2" xref="S2.E1.m1.1.1.3.2.cmml"><mi id="S2.E1.m1.1.1.3.2.2" xref="S2.E1.m1.1.1.3.2.2.cmml">E</mi><mrow id="S2.E1.m1.1.1.3.2.3" xref="S2.E1.m1.1.1.3.2.3.cmml"><mi id="S2.E1.m1.1.1.3.2.3.2" xref="S2.E1.m1.1.1.3.2.3.2.cmml">KS</mi><mo id="S2.E1.m1.1.1.3.2.3.1" xref="S2.E1.m1.1.1.3.2.3.1.cmml">-</mo><mi id="S2.E1.m1.1.1.3.2.3.3" xref="S2.E1.m1.1.1.3.2.3.3.cmml">DFT</mi></mrow></msub><mo id="S2.E1.m1.1.1.3.1" xref="S2.E1.m1.1.1.3.1.cmml">+</mo><msub id="S2.E1.m1.1.1.3.3" xref="S2.E1.m1.1.1.3.3.cmml"><mi id="S2.E1.m1.1.1.3.3.2" xref="S2.E1.m1.1.1.3.3.2.cmml">E</mi><mi id="S2.E1.m1.1.1.3.3.3" xref="S2.E1.m1.1.1.3.3.3.cmml">Disp</mi></msub></mrow></mrow></math>, <math><mrow id="S2.E2.m1.1.1" xref="S2.E2.m1.1.1.cmml"><msub id="S2.E2.m1.1.1.3" xref="S2.E2.m1.1.1.3.cmml"><mi id="S2.E2.m1.1.1.3.2" xref="S2.E2.m1.1.1.3.2.cmml">E</mi><mi id="S2.E2.m1.1.1.3.3" xref="S2.E2.m1.1.1.3.3.cmml">Disp</mi></msub><mo id="S2.E2.m1.1.1.2" xref="S2.E2.m1.1.1.2.cmml">=</mo><mrow 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xref="S2.E2.m1.1.1.1.1.1.1.1.1.1.1.cmml">)</mo></mrow></mrow></mrow></mrow></mrow></mrow></mrow></math>, <math><mrow id="S2.E3.m1.1.1" xref="S2.E3.m1.1.1.cmml"><msubsup id="S2.E3.m1.1.1.2" xref="S2.E3.m1.1.1.2.cmml"><mi id="S2.E3.m1.1.1.2.2.2" xref="S2.E3.m1.1.1.2.2.2.cmml">C</mi><mn id="S2.E3.m1.1.1.2.3" xref="S2.E3.m1.1.1.2.3.cmml">6</mn><mrow id="S2.E3.m1.1.1.2.2.3" xref="S2.E3.m1.1.1.2.2.3.cmml"><mi id="S2.E3.m1.1.1.2.2.3.2" xref="S2.E3.m1.1.1.2.2.3.2.cmml">i</mi><mo id="S2.E3.m1.1.1.2.2.3.1" xref="S2.E3.m1.1.1.2.2.3.1.cmml">⁢</mo><mi id="S2.E3.m1.1.1.2.2.3.3" xref="S2.E3.m1.1.1.2.2.3.3.cmml">j</mi></mrow></msubsup><mo id="S2.E3.m1.1.1.1" xref="S2.E3.m1.1.1.1.cmml">=</mo><msqrt id="S2.E3.m1.1.1.3" xref="S2.E3.m1.1.1.3.cmml"><mrow id="S2.E3.m1.1.1.3.2" xref="S2.E3.m1.1.1.3.2.cmml"><msubsup id="S2.E3.m1.1.1.3.2.2" xref="S2.E3.m1.1.1.3.2.2.cmml"><mi id="S2.E3.m1.1.1.3.2.2.2.2" xref="S2.E3.m1.1.1.3.2.2.2.2.cmml">C</mi><mn id="S2.E3.m1.1.1.3.2.2.3" xref="S2.E3.m1.1.1.3.2.2.3.cmml">6</mn><mi id="S2.E3.m1.1.1.3.2.2.2.3" xref="S2.E3.m1.1.1.3.2.2.2.3.cmml">i</mi></msubsup><mo id="S2.E3.m1.1.1.3.2.1" xref="S2.E3.m1.1.1.3.2.1.cmml">⁢</mo><msubsup id="S2.E3.m1.1.1.3.2.3" xref="S2.E3.m1.1.1.3.2.3.cmml"><mi id="S2.E3.m1.1.1.3.2.3.2.2" xref="S2.E3.m1.1.1.3.2.3.2.2.cmml">C</mi><mn id="S2.E3.m1.1.1.3.2.3.3" xref="S2.E3.m1.1.1.3.2.3.3.cmml">6</mn><mi id="S2.E3.m1.1.1.3.2.3.2.3" xref="S2.E3.m1.1.1.3.2.3.2.3.cmml">j</mi></msubsup></mrow></msqrt></mrow></math>, <math><mrow id="S2.p7.7.m4.1.1" xref="S2.p7.7.m4.1.1.cmml"><mi id="S2.p7.7.m4.1.1.2" xref="S2.p7.7.m4.1.1.2.cmml">N</mi><mo id="S2.p7.7.m4.1.1.1" xref="S2.p7.7.m4.1.1.1.cmml">⁢</mo><msubsup id="S2.p7.7.m4.1.1.3" xref="S2.p7.7.m4.1.1.3.cmml"><mi id="S2.p7.7.m4.1.1.3.2.2" xref="S2.p7.7.m4.1.1.3.2.2.cmml">I</mi><mi mathvariant="normal" id="S2.p7.7.m4.1.1.3.3" xref="S2.p7.7.m4.1.1.3.3.cmml">p</mi><mi id="S2.p7.7.m4.1.1.3.2.3" xref="S2.p7.7.m4.1.1.3.2.3.cmml">i</mi></msubsup><mo id="S2.p7.7.m4.1.1.1a" xref="S2.p7.7.m4.1.1.1.cmml">⁢</mo><msup id="S2.p7.7.m4.1.1.4" xref="S2.p7.7.m4.1.1.4.cmml"><mi id="S2.p7.7.m4.1.1.4.2" xref="S2.p7.7.m4.1.1.4.2.cmml">α</mi><mi id="S2.p7.7.m4.1.1.4.3" xref="S2.p7.7.m4.1.1.4.3.cmml">i</mi></msup></mrow></math>, <math><mrow id="S2.p7.15.m12.1.1" xref="S2.p7.15.m12.1.1.cmml"><msub id="S2.p7.15.m12.1.1.3" xref="S2.p7.15.m12.1.1.3.cmml"><mi id="S2.p7.15.m12.1.1.3.2" xref="S2.p7.15.m12.1.1.3.2.cmml">f</mi><mi id="S2.p7.15.m12.1.1.3.3" xref="S2.p7.15.m12.1.1.3.3.cmml">dmp</mi></msub><mo id="S2.p7.15.m12.1.1.2" xref="S2.p7.15.m12.1.1.2.cmml">⁢</mo><mrow id="S2.p7.15.m12.1.1.1.1" xref="S2.p7.15.m12.1.1.1.1.1.cmml"><mo stretchy="false" id="S2.p7.15.m12.1.1.1.1.2" xref="S2.p7.15.m12.1.1.1.1.1.cmml">(</mo><msub id="S2.p7.15.m12.1.1.1.1.1" xref="S2.p7.15.m12.1.1.1.1.1.cmml"><mi id="S2.p7.15.m12.1.1.1.1.1.2" xref="S2.p7.15.m12.1.1.1.1.1.2.cmml">R</mi><mrow id="S2.p7.15.m12.1.1.1.1.1.3" xref="S2.p7.15.m12.1.1.1.1.1.3.cmml"><mi id="S2.p7.15.m12.1.1.1.1.1.3.2" xref="S2.p7.15.m12.1.1.1.1.1.3.2.cmml">i</mi><mo id="S2.p7.15.m12.1.1.1.1.1.3.1" xref="S2.p7.15.m12.1.1.1.1.1.3.1.cmml">⁢</mo><mi id="S2.p7.15.m12.1.1.1.1.1.3.3" xref="S2.p7.15.m12.1.1.1.1.1.3.3.cmml">j</mi></mrow></msub><mo stretchy="false" id="S2.p7.15.m12.1.1.1.1.3" xref="S2.p7.15.m12.1.1.1.1.1.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S2.E4.m1.2.2" xref="S2.E4.m1.2.2.cmml"><mrow id="S2.E4.m1.2.2.1" xref="S2.E4.m1.2.2.1.cmml"><msub id="S2.E4.m1.2.2.1.3" xref="S2.E4.m1.2.2.1.3.cmml"><mi id="S2.E4.m1.2.2.1.3.2" xref="S2.E4.m1.2.2.1.3.2.cmml">f</mi><mi id="S2.E4.m1.2.2.1.3.3" xref="S2.E4.m1.2.2.1.3.3.cmml">dmp</mi></msub><mo id="S2.E4.m1.2.2.1.2" xref="S2.E4.m1.2.2.1.2.cmml">⁢</mo><mrow id="S2.E4.m1.2.2.1.1.1" xref="S2.E4.m1.2.2.1.1.1.1.cmml"><mo stretchy="false" id="S2.E4.m1.2.2.1.1.1.2" xref="S2.E4.m1.2.2.1.1.1.1.cmml">(</mo><msub id="S2.E4.m1.2.2.1.1.1.1" xref="S2.E4.m1.2.2.1.1.1.1.cmml"><mi id="S2.E4.m1.2.2.1.1.1.1.2" xref="S2.E4.m1.2.2.1.1.1.1.2.cmml">R</mi><mrow id="S2.E4.m1.2.2.1.1.1.1.3" xref="S2.E4.m1.2.2.1.1.1.1.3.cmml"><mi id="S2.E4.m1.2.2.1.1.1.1.3.2" xref="S2.E4.m1.2.2.1.1.1.1.3.2.cmml">i</mi><mo id="S2.E4.m1.2.2.1.1.1.1.3.1" xref="S2.E4.m1.2.2.1.1.1.1.3.1.cmml">⁢</mo><mi id="S2.E4.m1.2.2.1.1.1.1.3.3" xref="S2.E4.m1.2.2.1.1.1.1.3.3.cmml">j</mi></mrow></msub><mo stretchy="false" id="S2.E4.m1.2.2.1.1.1.3" xref="S2.E4.m1.2.2.1.1.1.1.cmml">)</mo></mrow></mrow><mo id="S2.E4.m1.2.2.2" xref="S2.E4.m1.2.2.2.cmml">=</mo><mfrac id="S2.E4.m1.1.1" xref="S2.E4.m1.1.1.cmml"><mn id="S2.E4.m1.1.1.3" xref="S2.E4.m1.1.1.3.cmml">1</mn><mrow id="S2.E4.m1.1.1.1" xref="S2.E4.m1.1.1.1.cmml"><mn id="S2.E4.m1.1.1.1.3" xref="S2.E4.m1.1.1.1.3.cmml">1</mn><mo id="S2.E4.m1.1.1.1.2" xref="S2.E4.m1.1.1.1.2.cmml">+</mo><msup id="S2.E4.m1.1.1.1.4" xref="S2.E4.m1.1.1.1.4.cmml"><mi id="S2.E4.m1.1.1.1.4.2" xref="S2.E4.m1.1.1.1.4.2.cmml">e</mi><mrow id="S2.E4.m1.1.1.1.1.1" xref="S2.E4.m1.1.1.1.1.1.cmml"><mo id="S2.E4.m1.1.1.1.1.1.2" xref="S2.E4.m1.1.1.1.1.1.2.cmml">-</mo><mrow id="S2.E4.m1.1.1.1.1.1.1" xref="S2.E4.m1.1.1.1.1.1.1.cmml"><mi id="S2.E4.m1.1.1.1.1.1.1.3" xref="S2.E4.m1.1.1.1.1.1.1.3.cmml">d</mi><mo id="S2.E4.m1.1.1.1.1.1.1.2" xref="S2.E4.m1.1.1.1.1.1.1.2.cmml">⁢</mo><mrow id="S2.E4.m1.1.1.1.1.1.1.1.1" xref="S2.E4.m1.1.1.1.1.1.1.1.1.1.cmml"><mo maxsize="171%" minsize="171%" id="S2.E4.m1.1.1.1.1.1.1.1.1.2" xref="S2.E4.m1.1.1.1.1.1.1.1.1.1.cmml">(</mo><mrow id="S2.E4.m1.1.1.1.1.1.1.1.1.1" xref="S2.E4.m1.1.1.1.1.1.1.1.1.1.cmml"><mfrac id="S2.E4.m1.1.1.1.1.1.1.1.1.1.2" xref="S2.E4.m1.1.1.1.1.1.1.1.1.1.2.cmml"><msub id="S2.E4.m1.1.1.1.1.1.1.1.1.1.2.2" xref="S2.E4.m1.1.1.1.1.1.1.1.1.1.2.2.cmml"><mi id="S2.E4.m1.1.1.1.1.1.1.1.1.1.2.2.2" xref="S2.E4.m1.1.1.1.1.1.1.1.1.1.2.2.2.cmml">R</mi><mrow id="S2.E4.m1.1.1.1.1.1.1.1.1.1.2.2.3" xref="S2.E4.m1.1.1.1.1.1.1.1.1.1.2.2.3.cmml"><mi id="S2.E4.m1.1.1.1.1.1.1.1.1.1.2.2.3.2" xref="S2.E4.m1.1.1.1.1.1.1.1.1.1.2.2.3.2.cmml">i</mi><mo id="S2.E4.m1.1.1.1.1.1.1.1.1.1.2.2.3.1" xref="S2.E4.m1.1.1.1.1.1.1.1.1.1.2.2.3.1.cmml">⁢</mo><mi id="S2.E4.m1.1.1.1.1.1.1.1.1.1.2.2.3.3" xref="S2.E4.m1.1.1.1.1.1.1.1.1.1.2.2.3.3.cmml">j</mi></mrow></msub><msub id="S2.E4.m1.1.1.1.1.1.1.1.1.1.2.3" xref="S2.E4.m1.1.1.1.1.1.1.1.1.1.2.3.cmml"><mi id="S2.E4.m1.1.1.1.1.1.1.1.1.1.2.3.2" xref="S2.E4.m1.1.1.1.1.1.1.1.1.1.2.3.2.cmml">R</mi><mi id="S2.E4.m1.1.1.1.1.1.1.1.1.1.2.3.3" xref="S2.E4.m1.1.1.1.1.1.1.1.1.1.2.3.3.cmml">r</mi></msub></mfrac><mo id="S2.E4.m1.1.1.1.1.1.1.1.1.1.1" xref="S2.E4.m1.1.1.1.1.1.1.1.1.1.1.cmml">-</mo><mn id="S2.E4.m1.1.1.1.1.1.1.1.1.1.3" xref="S2.E4.m1.1.1.1.1.1.1.1.1.1.3.cmml">1</mn></mrow><mo maxsize="171%" minsize="171%" id="S2.E4.m1.1.1.1.1.1.1.1.1.3" xref="S2.E4.m1.1.1.1.1.1.1.1.1.1.cmml">)</mo></mrow></mrow></mrow></msup></mrow></mfrac></mrow></math>, <math><mrow id="S2.E5.m1.4.5" xref="S2.E5.m1.4.5.cmml"><mrow id="S2.E5.m1.4.5.2" xref="S2.E5.m1.4.5.2.cmml"><mi mathvariant="normal" id="S2.E5.m1.4.5.2.2" xref="S2.E5.m1.4.5.2.2.cmml">Δ</mi><mo id="S2.E5.m1.4.5.2.1" xref="S2.E5.m1.4.5.2.1.cmml">⁢</mo><msub id="S2.E5.m1.4.5.2.3" xref="S2.E5.m1.4.5.2.3.cmml"><mi id="S2.E5.m1.4.5.2.3.2" xref="S2.E5.m1.4.5.2.3.2.cmml">E</mi><mi id="S2.E5.m1.4.5.2.3.3" xref="S2.E5.m1.4.5.2.3.3.cmml">ads</mi></msub></mrow><mo id="S2.E5.m1.4.5.1" xref="S2.E5.m1.4.5.1.cmml">=</mo><mrow id="S2.E5.m1.4.5.3" xref="S2.E5.m1.4.5.3.cmml"><msub id="S2.E5.m1.4.5.3.2" xref="S2.E5.m1.4.5.3.2.cmml"><mi id="S2.E5.m1.4.5.3.2.2" xref="S2.E5.m1.4.5.3.2.2.cmml">E</mi><mrow id="S2.E5.m1.1.1.1" xref="S2.E5.m1.1.1.1.cmml"><mi id="S2.E5.m1.1.1.1.3" xref="S2.E5.m1.1.1.1.3.cmml">system</mi><mo id="S2.E5.m1.1.1.1.2" xref="S2.E5.m1.1.1.1.2.cmml">⁢</mo><mrow id="S2.E5.m1.1.1.1.1.1" xref="S2.E5.m1.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S2.E5.m1.1.1.1.1.1.2" xref="S2.E5.m1.1.1.1.1.1.1.cmml">(</mo><mrow id="S2.E5.m1.1.1.1.1.1.1" xref="S2.E5.m1.1.1.1.1.1.1.cmml"><mi id="S2.E5.m1.1.1.1.1.1.1.2" xref="S2.E5.m1.1.1.1.1.1.1.2.cmml">MCPM</mi><mo id="S2.E5.m1.1.1.1.1.1.1.1" xref="S2.E5.m1.1.1.1.1.1.1.1.cmml">+</mo><msub id="S2.E5.m1.1.1.1.1.1.1.3" xref="S2.E5.m1.1.1.1.1.1.1.3.cmml"><mi id="S2.E5.m1.1.1.1.1.1.1.3.2" xref="S2.E5.m1.1.1.1.1.1.1.3.2.cmml">SiO</mi><mn id="S2.E5.m1.1.1.1.1.1.1.3.3" xref="S2.E5.m1.1.1.1.1.1.1.3.3.cmml">2</mn></msub></mrow><mo stretchy="false" id="S2.E5.m1.1.1.1.1.1.3" xref="S2.E5.m1.1.1.1.1.1.1.cmml">)</mo></mrow></mrow></msub><mo id="S2.E5.m1.4.5.3.1" xref="S2.E5.m1.4.5.3.1.cmml">-</mo><msub id="S2.E5.m1.4.5.3.3" xref="S2.E5.m1.4.5.3.3.cmml"><mi id="S2.E5.m1.4.5.3.3.2" xref="S2.E5.m1.4.5.3.3.2.cmml">E</mi><mrow id="S2.E5.m1.3.3.2" xref="S2.E5.m1.3.3.2.cmml"><mi id="S2.E5.m1.3.3.2.4" xref="S2.E5.m1.3.3.2.4.cmml">molecule</mi><mo id="S2.E5.m1.3.3.2.3" xref="S2.E5.m1.3.3.2.3.cmml">⁢</mo><mrow id="S2.E5.m1.3.3.2.5.2" xref="S2.E5.m1.3.3.2.5.1.cmml"><mo stretchy="false" id="S2.E5.m1.3.3.2.5.2.1" xref="S2.E5.m1.3.3.2.5.1.cmml">(</mo><mi id="S2.E5.m1.2.2.1.1" xref="S2.E5.m1.2.2.1.1.cmml">MCPM</mi><mo rspace="4.7pt" id="S2.E5.m1.3.3.2.5.2.2" xref="S2.E5.m1.3.3.2.5.1.cmml">,</mo><mi mathvariant="normal" id="S2.E5.m1.3.3.2.2" xref="S2.E5.m1.3.3.2.2.cmml">g</mi><mo stretchy="false" id="S2.E5.m1.3.3.2.5.2.3" xref="S2.E5.m1.3.3.2.5.1.cmml">)</mo></mrow></mrow></msub><mo id="S2.E5.m1.4.5.3.1a" xref="S2.E5.m1.4.5.3.1.cmml">-</mo><msub id="S2.E5.m1.4.5.3.4" xref="S2.E5.m1.4.5.3.4.cmml"><mi id="S2.E5.m1.4.5.3.4.2" xref="S2.E5.m1.4.5.3.4.2.cmml">E</mi><mrow id="S2.E5.m1.4.4.1" xref="S2.E5.m1.4.4.1.cmml"><mpadded width="+2.2pt" id="S2.E5.m1.4.4.1.3" xref="S2.E5.m1.4.4.1.3.cmml"><mi id="S2.E5.m1.4.4.1.3a" xref="S2.E5.m1.4.4.1.3.cmml">clean</mi></mpadded><mo id="S2.E5.m1.4.4.1.2" xref="S2.E5.m1.4.4.1.2.cmml">⁢</mo><mi id="S2.E5.m1.4.4.1.4" xref="S2.E5.m1.4.4.1.4.cmml">surface</mi><mo id="S2.E5.m1.4.4.1.2a" xref="S2.E5.m1.4.4.1.2.cmml">⁢</mo><mrow id="S2.E5.m1.4.4.1.1.1" xref="S2.E5.m1.4.4.1.1.1.1.cmml"><mo stretchy="false" id="S2.E5.m1.4.4.1.1.1.2" xref="S2.E5.m1.4.4.1.1.1.1.cmml">(</mo><msub id="S2.E5.m1.4.4.1.1.1.1" xref="S2.E5.m1.4.4.1.1.1.1.cmml"><mi id="S2.E5.m1.4.4.1.1.1.1.2" xref="S2.E5.m1.4.4.1.1.1.1.2.cmml">SiO</mi><mn id="S2.E5.m1.4.4.1.1.1.1.3" xref="S2.E5.m1.4.4.1.1.1.1.3.cmml">2</mn></msub><mo stretchy="false" id="S2.E5.m1.4.4.1.1.1.3" xref="S2.E5.m1.4.4.1.1.1.1.cmml">)</mo></mrow></mrow></msub></mrow></mrow></math>, <math><msub id="S2.p8.2.m2.1.2" xref="S2.p8.2.m2.1.2.cmml"><mi id="S2.p8.2.m2.1.2.2" xref="S2.p8.2.m2.1.2.2.cmml">E</mi><mrow id="S2.p8.2.m2.1.1.1" xref="S2.p8.2.m2.1.1.1.cmml"><mi id="S2.p8.2.m2.1.1.1.3" xref="S2.p8.2.m2.1.1.1.3.cmml">system</mi><mo id="S2.p8.2.m2.1.1.1.2" xref="S2.p8.2.m2.1.1.1.2.cmml">⁢</mo><mrow id="S2.p8.2.m2.1.1.1.1.1" xref="S2.p8.2.m2.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S2.p8.2.m2.1.1.1.1.1.2" xref="S2.p8.2.m2.1.1.1.1.1.1.cmml">(</mo><mrow id="S2.p8.2.m2.1.1.1.1.1.1" xref="S2.p8.2.m2.1.1.1.1.1.1.cmml"><mi id="S2.p8.2.m2.1.1.1.1.1.1.2" 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Correct Categorie: cond-mat

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/gr-qc/9608050

Formulas:

1-

d s^{2} = - (1 - \frac{2 M}{r}) d t^{2} + {(1 - \frac{2 M}{r})}^{- 1} d r^{2} + r^{2} d Ω^{2},

2-

\bar{r} {(1 + \frac{M}{2 \bar{r}})}^{2},

3-

- α {(\bar{r})}^{2} d t^{2} + ψ {(\bar{r})}^{4} (d {\bar{r}}^{2} + {\bar{r}}^{2} d Ω^{2}),

4-

α (\bar{r})

5-

(1 - \frac{M}{2 \bar{r}}) / (1 + \frac{M}{2 \bar{r}}),

6-

ψ (\bar{r})

7-

1 + \frac{M}{2 \bar{r}} .

8-

d x^{2} + d y^{2} + d z^{2} = d {\bar{r}}^{2} + {\bar{r}}^{2} d Ω^{2}, \bar{r} = {(x^{2} + y^{2} + z^{2})}^{1 / 2} .

9-

\bar{r} = M / 2

10-

\bar{r} \leftrightarrow {\bar{r}}^{'} = M^{2} / (4 \bar{r})

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: hep-th

Result: incorrect

Paper: https://arxiv.org/abs/hep-ph/0512336

Formulas:

1-

{(0 s)}^{3}

2-

S U (6)

3-

I {(J)}^{P} = 1 / 2 {(1 / 2)}^{+}

4-

𝓁 = {\bar{χ}}_{c} (i / \partial - m_{q}) χ_{c} + D_{c}^{†} (\partial^{2} + M_{S}^{2}) D_{c} + {\vec{D}}^{† μ}_{c} [(\partial^{2} + M_{A}^{2}) g_{μ ν} - \partial_{μ} \partial_{ν}] {\vec{D}}_{c}^{ν} + L_{i n t},

5-

L_{i n t}

6-

L_{i n t}

7-

G_{S} {\bar{χ}}_{c} D_{c}^{†} D_{c^{'}} χ_{c^{'}} + v ({\bar{χ}}_{c} D_{c}^{†} γ^{μ} γ^{5} \vec{τ} \cdot {\vec{D}}_{μ c^{'}} χ_{c^{'}} + {\bar{χ}}_{c} γ^{μ} γ^{5} \vec{τ} \cdot {\vec{D}}_{μ c}^{†} D_{c^{'}} χ_{c^{'}})

8-

G_{A} {\bar{χ}}_{c} γ^{μ} γ^{5} \vec{τ} \cdot {\vec{D}}_{μ c}^{†} \vec{τ} \cdot {\vec{D}}_{ν c^{'}} γ^{ν} γ^{5} χ_{c^{'}},

9-

M_{1, 2} = \frac{1}{2} [a_{S} + a_{A} \pm \sqrt{{(a_{S} - a_{A})}^{2} + 4 Z_{S} Z_{A} {(\frac{v}{| \hat{G} |})}^{2}}],

10-

Σ_{S} (p_{0}) - \frac{1}{| \hat{G} |} G_{A}

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: hep-ph

Result: correct

Paper: https://arxiv.org/abs/cond-mat/9812339

Formulas:

1-

6 < r_{s} < 9

2-

| I_{t} / I_{l} | \approx \exp - (r_{s} / r_{s}^{F})

3-

I_{l} \approx \exp - (r_{s} / r_{s}^{W})

4-

r_{s}^{F} < r_{s}^{W}

5-

(r_{s}^{F} < r_{s} < r_{s}^{W})

6-

r_{s} > r_{s}^{F}

7-

r_{s} \approx 8 - 10

8-

H = - t \sum_{< i, j >} c_{i}^{†} c_{j} + \sum_{i} v_{i} n_{i} + \frac{U}{2} \sum_{i \neq j} \frac{1}{r_{i j}} (n_{i} n_{j}),

9-

i = (i_{x}, i_{y})

10-

\sum_{< i, j >}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cs

Result: incorrect

Paper: https://arxiv.org/abs/1810.03790

Formulas:

1-

k_{G I S T}

2-

k_{L D B}

3-

k_{B o W}

4-

k = k_{G I S T} + k_{B o W} + k_{L D B}

5-

k_{G I S T} = k_{B o W} = k_{L D B} = 5

6-

P r e c i s i o n = \frac{T P}{T P + F P}

7-

R e c a l l = \frac{T P}{T P + F N}

8-

k_{G I S T}

9-

k_{L D B}

10-

k_{B o W}

Formulas (html):

Correct Categorie: cs

Guessed Categorie: cs

Result: correct

Run 6969985 (Agent182)