Run 12593918

Paper: https://arxiv.org/abs/1202.5626

Formulas:

1-

{x \circ y} = H x y \cap S

2-

𝒯 (G, H)

3-

T \in 𝒯 (G, H)

4-

S \in 𝒯 (G, H)

5-

S \in 𝒯 (G, H)

6-

R_{x}^{- 1} = R_{r (x)}

7-

(x, y) \in S \times S

8-

R_{x} R_{y} R_{x}^{- 1} = R_{z}

9-

H \subseteq N_{G} (S)

10-

N_{G} (S)

Formulas (html):

Correct Categorie: math

Guessed Categorie: math

Result: correct

Paper: https://arxiv.org/abs/1901.03067

Formulas:

1-

P = {p_{1}, p_{2}, \dots, p_{N}}

2-

O = {o_{1}, o_{2}, \dots, o_{M}}

3-

A_{o} \in ℝ^{(N + M) \times (N + M)}

4-

A_{o} (p_{i}, o_{j}) = {\begin{matrix} 1 & I o U (p_{i} (k), o_{j}) > 0, \\ 0 & o t h e r s i s e, \end{matrix}

5-

I o U (\cdot, \cdot)

6-

p_{i} (k)

7-

A_{p} \in ℝ^{(2 K) \times (2 K)}

8-

2 - d i s t (p_{1} (k), p_{2} (k^{'}))

9-

d i s t (\cdot, \cdot)

10-

X^{(l + 1)} = σ ({\tilde{D}}^{- \frac{1}{2}} \tilde{A} {\tilde{D}}^{- \frac{1}{2}} X^{(l)} W^{(l)}),

Formulas (html):

Correct Categorie: cs

Guessed Categorie: gr-qc

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0702396

Formulas:

1-

M (τ) = 3 / 4

2-

2 / 3 - B_{i, m i n}

3-

M (T_{c})

4-

χ^{m a x} (L)

5-

χ (T_{c})

6-

p_{i} = 1 / 1 + \exp (2 E_{i} / k_{B} T), E_{i} = - J \sum_{k} S_{i} S_{k}

7-

m = \sum_{i = 1}^{N} S_{i} / N

8-

1 / \ln (τ) \propto T + \dots

9-

E = 2 \sum_{i} E_{i}

10-

m = \sum_{i = 1}^{N} S_{i} / N .

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: cond-mat

Result: correct

Paper: https://arxiv.org/abs/1511.08901

Formulas:

1-

[Fe / H] [dex]

2-

T_{eff} [K]

3-

M_{*} [M_{⊙}]

4-

R_{*} [R_{⊙}]

5-

\log (g_{*}) [cgs]

6-

M_{p} [M_{\oplus}]

7-

T_{eq} [K]

8-

R_{p} [R_{\oplus}]

9-

T_{0} [BJD]

10-

R p / R_{*}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/2008.00267

Formulas:

1-

I^{shadow-free} = I^{relit} \cdot α + I^{shadow} \cdot (1 - α)

2-

I_{i}^{relit} = w \cdot I_{i}^{shadow} + b

3-

[1; s_{m a x}]

4-

[- c, c]

5-

s_{m a x} = 10

6-

I_{i}^{output} = I_{i}^{relit} \cdot α_{i} + I_{i}^{shadow} \cdot (1 - α_{i})

7-

ℳ_{o u t}

8-

ℳ_{o u t}

9-

ℳ_{d i l a t e d}

10-

ℳ_{o u t}

Formulas (html):

<math><mrow id="S3.E1.m1.1.1" xref="S3.E1.m1.1.1.cmml"><msup id="S3.E1.m1.1.1.3" xref="S3.E1.m1.1.1.3.cmml"><mi id="S3.E1.m1.1.1.3.2" xref="S3.E1.m1.1.1.3.2.cmml">I</mi><mtext id="S3.E1.m1.1.1.3.3" xref="S3.E1.m1.1.1.3.3a.cmml">shadow-free</mtext></msup><mo id="S3.E1.m1.1.1.2" xref="S3.E1.m1.1.1.2.cmml">=</mo><mrow id="S3.E1.m1.1.1.1" xref="S3.E1.m1.1.1.1.cmml"><mrow id="S3.E1.m1.1.1.1.3" xref="S3.E1.m1.1.1.1.3.cmml"><msup id="S3.E1.m1.1.1.1.3.2" xref="S3.E1.m1.1.1.1.3.2.cmml"><mi id="S3.E1.m1.1.1.1.3.2.2" xref="S3.E1.m1.1.1.1.3.2.2.cmml">I</mi><mtext id="S3.E1.m1.1.1.1.3.2.3" xref="S3.E1.m1.1.1.1.3.2.3a.cmml">relit</mtext></msup><mo id="S3.E1.m1.1.1.1.3.1" xref="S3.E1.m1.1.1.1.3.1.cmml">⋅</mo><mi id="S3.E1.m1.1.1.1.3.3" xref="S3.E1.m1.1.1.1.3.3.cmml">α</mi></mrow><mo id="S3.E1.m1.1.1.1.2" xref="S3.E1.m1.1.1.1.2.cmml">+</mo><mrow id="S3.E1.m1.1.1.1.1" xref="S3.E1.m1.1.1.1.1.cmml"><msup id="S3.E1.m1.1.1.1.1.3" xref="S3.E1.m1.1.1.1.1.3.cmml"><mi id="S3.E1.m1.1.1.1.1.3.2" xref="S3.E1.m1.1.1.1.1.3.2.cmml">I</mi><mtext id="S3.E1.m1.1.1.1.1.3.3" xref="S3.E1.m1.1.1.1.1.3.3a.cmml">shadow</mtext></msup><mo id="S3.E1.m1.1.1.1.1.2" xref="S3.E1.m1.1.1.1.1.2.cmml">⋅</mo><mrow id="S3.E1.m1.1.1.1.1.1.1" xref="S3.E1.m1.1.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S3.E1.m1.1.1.1.1.1.1.2" xref="S3.E1.m1.1.1.1.1.1.1.1.cmml">(</mo><mrow id="S3.E1.m1.1.1.1.1.1.1.1" xref="S3.E1.m1.1.1.1.1.1.1.1.cmml"><mn id="S3.E1.m1.1.1.1.1.1.1.1.2" xref="S3.E1.m1.1.1.1.1.1.1.1.2.cmml">1</mn><mo id="S3.E1.m1.1.1.1.1.1.1.1.1" xref="S3.E1.m1.1.1.1.1.1.1.1.1.cmml">-</mo><mi id="S3.E1.m1.1.1.1.1.1.1.1.3" xref="S3.E1.m1.1.1.1.1.1.1.1.3.cmml">α</mi></mrow><mo stretchy="false" id="S3.E1.m1.1.1.1.1.1.1.3" xref="S3.E1.m1.1.1.1.1.1.1.1.cmml">)</mo></mrow></mrow></mrow></mrow></math>, <math><mrow id="S3.E2.m1.1.1" xref="S3.E2.m1.1.1.cmml"><msubsup id="S3.E2.m1.1.1.2" xref="S3.E2.m1.1.1.2.cmml"><mi id="S3.E2.m1.1.1.2.2.2" xref="S3.E2.m1.1.1.2.2.2.cmml">I</mi><mi id="S3.E2.m1.1.1.2.2.3" xref="S3.E2.m1.1.1.2.2.3.cmml">i</mi><mtext id="S3.E2.m1.1.1.2.3" xref="S3.E2.m1.1.1.2.3a.cmml">relit</mtext></msubsup><mo id="S3.E2.m1.1.1.1" xref="S3.E2.m1.1.1.1.cmml">=</mo><mrow id="S3.E2.m1.1.1.3" xref="S3.E2.m1.1.1.3.cmml"><mrow id="S3.E2.m1.1.1.3.2" xref="S3.E2.m1.1.1.3.2.cmml"><mi id="S3.E2.m1.1.1.3.2.2" xref="S3.E2.m1.1.1.3.2.2.cmml">w</mi><mo id="S3.E2.m1.1.1.3.2.1" xref="S3.E2.m1.1.1.3.2.1.cmml">⋅</mo><msubsup id="S3.E2.m1.1.1.3.2.3" xref="S3.E2.m1.1.1.3.2.3.cmml"><mi id="S3.E2.m1.1.1.3.2.3.2.2" xref="S3.E2.m1.1.1.3.2.3.2.2.cmml">I</mi><mi id="S3.E2.m1.1.1.3.2.3.2.3" xref="S3.E2.m1.1.1.3.2.3.2.3.cmml">i</mi><mtext id="S3.E2.m1.1.1.3.2.3.3" xref="S3.E2.m1.1.1.3.2.3.3a.cmml">shadow</mtext></msubsup></mrow><mo id="S3.E2.m1.1.1.3.1" xref="S3.E2.m1.1.1.3.1.cmml">+</mo><mi id="S3.E2.m1.1.1.3.3" xref="S3.E2.m1.1.1.3.3.cmml">b</mi></mrow></mrow></math>, <math><mrow id="S3.SS1.p3.4.m4.2.2.1" xref="S3.SS1.p3.4.m4.2.2.2.cmml"><mo stretchy="false" id="S3.SS1.p3.4.m4.2.2.1.2" xref="S3.SS1.p3.4.m4.2.2.2.cmml">[</mo><mn id="S3.SS1.p3.4.m4.1.1" xref="S3.SS1.p3.4.m4.1.1.cmml">1</mn><mo id="S3.SS1.p3.4.m4.2.2.1.3" xref="S3.SS1.p3.4.m4.2.2.2.cmml">;</mo><msub id="S3.SS1.p3.4.m4.2.2.1.1" xref="S3.SS1.p3.4.m4.2.2.1.1.cmml"><mi id="S3.SS1.p3.4.m4.2.2.1.1.2" xref="S3.SS1.p3.4.m4.2.2.1.1.2.cmml">s</mi><mrow id="S3.SS1.p3.4.m4.2.2.1.1.3" xref="S3.SS1.p3.4.m4.2.2.1.1.3.cmml"><mi id="S3.SS1.p3.4.m4.2.2.1.1.3.2" xref="S3.SS1.p3.4.m4.2.2.1.1.3.2.cmml">m</mi><mo id="S3.SS1.p3.4.m4.2.2.1.1.3.1" xref="S3.SS1.p3.4.m4.2.2.1.1.3.1.cmml">⁢</mo><mi id="S3.SS1.p3.4.m4.2.2.1.1.3.3" xref="S3.SS1.p3.4.m4.2.2.1.1.3.3.cmml">a</mi><mo id="S3.SS1.p3.4.m4.2.2.1.1.3.1a" xref="S3.SS1.p3.4.m4.2.2.1.1.3.1.cmml">⁢</mo><mi id="S3.SS1.p3.4.m4.2.2.1.1.3.4" xref="S3.SS1.p3.4.m4.2.2.1.1.3.4.cmml">x</mi></mrow></msub><mo stretchy="false" id="S3.SS1.p3.4.m4.2.2.1.4" xref="S3.SS1.p3.4.m4.2.2.2.cmml">]</mo></mrow></math>, <math><mrow id="S3.SS1.p3.7.m7.2.2.1" xref="S3.SS1.p3.7.m7.2.2.2.cmml"><mo stretchy="false" id="S3.SS1.p3.7.m7.2.2.1.2" xref="S3.SS1.p3.7.m7.2.2.2.cmml">[</mo><mrow id="S3.SS1.p3.7.m7.2.2.1.1" xref="S3.SS1.p3.7.m7.2.2.1.1.cmml"><mo id="S3.SS1.p3.7.m7.2.2.1.1.1" xref="S3.SS1.p3.7.m7.2.2.1.1.1.cmml">-</mo><mi id="S3.SS1.p3.7.m7.2.2.1.1.2" xref="S3.SS1.p3.7.m7.2.2.1.1.2.cmml">c</mi></mrow><mo id="S3.SS1.p3.7.m7.2.2.1.3" xref="S3.SS1.p3.7.m7.2.2.2.cmml">,</mo><mi id="S3.SS1.p3.7.m7.1.1" xref="S3.SS1.p3.7.m7.1.1.cmml">c</mi><mo stretchy="false" id="S3.SS1.p3.7.m7.2.2.1.4" xref="S3.SS1.p3.7.m7.2.2.2.cmml">]</mo></mrow></math>, <math><mrow id="S3.SS1.p3.10.m10.1.1" xref="S3.SS1.p3.10.m10.1.1.cmml"><msub id="S3.SS1.p3.10.m10.1.1.2" xref="S3.SS1.p3.10.m10.1.1.2.cmml"><mi id="S3.SS1.p3.10.m10.1.1.2.2" xref="S3.SS1.p3.10.m10.1.1.2.2.cmml">s</mi><mrow id="S3.SS1.p3.10.m10.1.1.2.3" xref="S3.SS1.p3.10.m10.1.1.2.3.cmml"><mi id="S3.SS1.p3.10.m10.1.1.2.3.2" xref="S3.SS1.p3.10.m10.1.1.2.3.2.cmml">m</mi><mo id="S3.SS1.p3.10.m10.1.1.2.3.1" xref="S3.SS1.p3.10.m10.1.1.2.3.1.cmml">⁢</mo><mi id="S3.SS1.p3.10.m10.1.1.2.3.3" xref="S3.SS1.p3.10.m10.1.1.2.3.3.cmml">a</mi><mo id="S3.SS1.p3.10.m10.1.1.2.3.1a" xref="S3.SS1.p3.10.m10.1.1.2.3.1.cmml">⁢</mo><mi id="S3.SS1.p3.10.m10.1.1.2.3.4" xref="S3.SS1.p3.10.m10.1.1.2.3.4.cmml">x</mi></mrow></msub><mo id="S3.SS1.p3.10.m10.1.1.1" xref="S3.SS1.p3.10.m10.1.1.1.cmml">=</mo><mn id="S3.SS1.p3.10.m10.1.1.3" xref="S3.SS1.p3.10.m10.1.1.3.cmml">10</mn></mrow></math>, <math><mrow id="S3.E3.m1.1.1" xref="S3.E3.m1.1.1.cmml"><msubsup id="S3.E3.m1.1.1.3" xref="S3.E3.m1.1.1.3.cmml"><mi id="S3.E3.m1.1.1.3.2.2" xref="S3.E3.m1.1.1.3.2.2.cmml">I</mi><mi id="S3.E3.m1.1.1.3.2.3" xref="S3.E3.m1.1.1.3.2.3.cmml">i</mi><mtext id="S3.E3.m1.1.1.3.3" xref="S3.E3.m1.1.1.3.3a.cmml">output</mtext></msubsup><mo id="S3.E3.m1.1.1.2" xref="S3.E3.m1.1.1.2.cmml">=</mo><mrow id="S3.E3.m1.1.1.1" xref="S3.E3.m1.1.1.1.cmml"><mrow id="S3.E3.m1.1.1.1.3" xref="S3.E3.m1.1.1.1.3.cmml"><msubsup id="S3.E3.m1.1.1.1.3.2" xref="S3.E3.m1.1.1.1.3.2.cmml"><mi id="S3.E3.m1.1.1.1.3.2.2.2" xref="S3.E3.m1.1.1.1.3.2.2.2.cmml">I</mi><mi id="S3.E3.m1.1.1.1.3.2.2.3" xref="S3.E3.m1.1.1.1.3.2.2.3.cmml">i</mi><mtext id="S3.E3.m1.1.1.1.3.2.3" xref="S3.E3.m1.1.1.1.3.2.3a.cmml">relit</mtext></msubsup><mo id="S3.E3.m1.1.1.1.3.1" xref="S3.E3.m1.1.1.1.3.1.cmml">⋅</mo><msub id="S3.E3.m1.1.1.1.3.3" xref="S3.E3.m1.1.1.1.3.3.cmml"><mi id="S3.E3.m1.1.1.1.3.3.2" xref="S3.E3.m1.1.1.1.3.3.2.cmml">α</mi><mi id="S3.E3.m1.1.1.1.3.3.3" xref="S3.E3.m1.1.1.1.3.3.3.cmml">i</mi></msub></mrow><mo id="S3.E3.m1.1.1.1.2" xref="S3.E3.m1.1.1.1.2.cmml">+</mo><mrow id="S3.E3.m1.1.1.1.1" xref="S3.E3.m1.1.1.1.1.cmml"><msubsup id="S3.E3.m1.1.1.1.1.3" xref="S3.E3.m1.1.1.1.1.3.cmml"><mi id="S3.E3.m1.1.1.1.1.3.2.2" xref="S3.E3.m1.1.1.1.1.3.2.2.cmml">I</mi><mi id="S3.E3.m1.1.1.1.1.3.2.3" xref="S3.E3.m1.1.1.1.1.3.2.3.cmml">i</mi><mtext id="S3.E3.m1.1.1.1.1.3.3" xref="S3.E3.m1.1.1.1.1.3.3a.cmml">shadow</mtext></msubsup><mo id="S3.E3.m1.1.1.1.1.2" xref="S3.E3.m1.1.1.1.1.2.cmml">⋅</mo><mrow id="S3.E3.m1.1.1.1.1.1.1" xref="S3.E3.m1.1.1.1.1.1.1.1.cmml"><mo stretchy="false" id="S3.E3.m1.1.1.1.1.1.1.2" xref="S3.E3.m1.1.1.1.1.1.1.1.cmml">(</mo><mrow id="S3.E3.m1.1.1.1.1.1.1.1" xref="S3.E3.m1.1.1.1.1.1.1.1.cmml"><mn id="S3.E3.m1.1.1.1.1.1.1.1.2" xref="S3.E3.m1.1.1.1.1.1.1.1.2.cmml">1</mn><mo id="S3.E3.m1.1.1.1.1.1.1.1.1" xref="S3.E3.m1.1.1.1.1.1.1.1.1.cmml">-</mo><msub id="S3.E3.m1.1.1.1.1.1.1.1.3" xref="S3.E3.m1.1.1.1.1.1.1.1.3.cmml"><mi id="S3.E3.m1.1.1.1.1.1.1.1.3.2" xref="S3.E3.m1.1.1.1.1.1.1.1.3.2.cmml">α</mi><mi id="S3.E3.m1.1.1.1.1.1.1.1.3.3" xref="S3.E3.m1.1.1.1.1.1.1.1.3.3.cmml">i</mi></msub></mrow><mo stretchy="false" id="S3.E3.m1.1.1.1.1.1.1.3" xref="S3.E3.m1.1.1.1.1.1.1.1.cmml">)</mo></mrow></mrow></mrow></mrow></math>, <math><msub id="S3.SS1.p5.2.m2.1.1" xref="S3.SS1.p5.2.m2.1.1.cmml"><mi class="ltx_font_mathcaligraphic" id="S3.SS1.p5.2.m2.1.1.2" xref="S3.SS1.p5.2.m2.1.1.2.cmml">ℳ</mi><mrow id="S3.SS1.p5.2.m2.1.1.3" xref="S3.SS1.p5.2.m2.1.1.3.cmml"><mi id="S3.SS1.p5.2.m2.1.1.3.2" xref="S3.SS1.p5.2.m2.1.1.3.2.cmml">o</mi><mo id="S3.SS1.p5.2.m2.1.1.3.1" xref="S3.SS1.p5.2.m2.1.1.3.1.cmml">⁢</mo><mi id="S3.SS1.p5.2.m2.1.1.3.3" xref="S3.SS1.p5.2.m2.1.1.3.3.cmml">u</mi><mo id="S3.SS1.p5.2.m2.1.1.3.1a" xref="S3.SS1.p5.2.m2.1.1.3.1.cmml">⁢</mo><mi id="S3.SS1.p5.2.m2.1.1.3.4" xref="S3.SS1.p5.2.m2.1.1.3.4.cmml">t</mi></mrow></msub></math>, <math><msub id="S3.SS1.p5.3.m3.1.1" xref="S3.SS1.p5.3.m3.1.1.cmml"><mi class="ltx_font_mathcaligraphic" id="S3.SS1.p5.3.m3.1.1.2" xref="S3.SS1.p5.3.m3.1.1.2.cmml">ℳ</mi><mrow id="S3.SS1.p5.3.m3.1.1.3" xref="S3.SS1.p5.3.m3.1.1.3.cmml"><mi id="S3.SS1.p5.3.m3.1.1.3.2" xref="S3.SS1.p5.3.m3.1.1.3.2.cmml">o</mi><mo id="S3.SS1.p5.3.m3.1.1.3.1" xref="S3.SS1.p5.3.m3.1.1.3.1.cmml">⁢</mo><mi id="S3.SS1.p5.3.m3.1.1.3.3" xref="S3.SS1.p5.3.m3.1.1.3.3.cmml">u</mi><mo id="S3.SS1.p5.3.m3.1.1.3.1a" xref="S3.SS1.p5.3.m3.1.1.3.1.cmml">⁢</mo><mi id="S3.SS1.p5.3.m3.1.1.3.4" xref="S3.SS1.p5.3.m3.1.1.3.4.cmml">t</mi></mrow></msub></math>, <math><msub id="S3.SS1.p5.5.m5.1.1" xref="S3.SS1.p5.5.m5.1.1.cmml"><mi class="ltx_font_mathcaligraphic" id="S3.SS1.p5.5.m5.1.1.2" xref="S3.SS1.p5.5.m5.1.1.2.cmml">ℳ</mi><mrow id="S3.SS1.p5.5.m5.1.1.3" xref="S3.SS1.p5.5.m5.1.1.3.cmml"><mi id="S3.SS1.p5.5.m5.1.1.3.2" xref="S3.SS1.p5.5.m5.1.1.3.2.cmml">d</mi><mo id="S3.SS1.p5.5.m5.1.1.3.1" xref="S3.SS1.p5.5.m5.1.1.3.1.cmml">⁢</mo><mi id="S3.SS1.p5.5.m5.1.1.3.3" xref="S3.SS1.p5.5.m5.1.1.3.3.cmml">i</mi><mo id="S3.SS1.p5.5.m5.1.1.3.1a" xref="S3.SS1.p5.5.m5.1.1.3.1.cmml">⁢</mo><mi id="S3.SS1.p5.5.m5.1.1.3.4" xref="S3.SS1.p5.5.m5.1.1.3.4.cmml">l</mi><mo id="S3.SS1.p5.5.m5.1.1.3.1b" xref="S3.SS1.p5.5.m5.1.1.3.1.cmml">⁢</mo><mi id="S3.SS1.p5.5.m5.1.1.3.5" xref="S3.SS1.p5.5.m5.1.1.3.5.cmml">a</mi><mo id="S3.SS1.p5.5.m5.1.1.3.1c" xref="S3.SS1.p5.5.m5.1.1.3.1.cmml">⁢</mo><mi id="S3.SS1.p5.5.m5.1.1.3.6" xref="S3.SS1.p5.5.m5.1.1.3.6.cmml">t</mi><mo id="S3.SS1.p5.5.m5.1.1.3.1d" xref="S3.SS1.p5.5.m5.1.1.3.1.cmml">⁢</mo><mi id="S3.SS1.p5.5.m5.1.1.3.7" xref="S3.SS1.p5.5.m5.1.1.3.7.cmml">e</mi><mo id="S3.SS1.p5.5.m5.1.1.3.1e" xref="S3.SS1.p5.5.m5.1.1.3.1.cmml">⁢</mo><mi id="S3.SS1.p5.5.m5.1.1.3.8" xref="S3.SS1.p5.5.m5.1.1.3.8.cmml">d</mi></mrow></msub></math>, <math><msub id="S3.SS1.p5.8.m8.1.1" xref="S3.SS1.p5.8.m8.1.1.cmml"><mi class="ltx_font_mathcaligraphic" id="S3.SS1.p5.8.m8.1.1.2" xref="S3.SS1.p5.8.m8.1.1.2.cmml">ℳ</mi><mrow id="S3.SS1.p5.8.m8.1.1.3" xref="S3.SS1.p5.8.m8.1.1.3.cmml"><mi id="S3.SS1.p5.8.m8.1.1.3.2" xref="S3.SS1.p5.8.m8.1.1.3.2.cmml">o</mi><mo id="S3.SS1.p5.8.m8.1.1.3.1" xref="S3.SS1.p5.8.m8.1.1.3.1.cmml">⁢</mo><mi id="S3.SS1.p5.8.m8.1.1.3.3" xref="S3.SS1.p5.8.m8.1.1.3.3.cmml">u</mi><mo id="S3.SS1.p5.8.m8.1.1.3.1a" xref="S3.SS1.p5.8.m8.1.1.3.1.cmml">⁢</mo><mi id="S3.SS1.p5.8.m8.1.1.3.4" xref="S3.SS1.p5.8.m8.1.1.3.4.cmml">t</mi></mrow></msub></math>

Correct Categorie: cs

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1902.06217

Formulas:

1-

(x, y, z)

2-

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

3-

0.5 𝐚 \pm 0.5 𝐛 + 0.1 𝐜

4-

P m m n

5-

U_{eff} = U - J

6-

ϵ_{n} = \frac{\int g_{n} (E) E d E}{\int g_{n} (E) d E}

7-

g_{n} (E)

8-

n \in {d_{x^{2} - y^{2}}, d_{x z}, d_{y z}, d_{z^{2}}, d_{x y}}

9-

E_{010} - E_{100} = 0.07

10-

E_{001} - E_{100} = 0.14

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: hep-lat

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/9611094

Formulas:

1-

0.484 ≲ Y_{e} ≲ 0.488

2-

4 π r^{2} ρ v,

3-

v \frac{d v}{d r}

4-

- \frac{1}{ρ} \frac{d P}{d r} - \frac{G M}{r^{2}},

5-

v (\frac{d ϵ}{d r} - \frac{P}{ρ^{2}} \frac{d ρ}{d r}),

6-

\frac{11 π^{2}}{180} T^{4} (1 + \frac{30 η^{2}}{11 π^{2}} + \frac{15 η^{4}}{11 π^{4}}) + \frac{ρ}{m_{N}} T,

7-

\frac{11 π^{2}}{60} \frac{T^{4}}{ρ} (1 + \frac{30 η^{2}}{11 π^{2}} + \frac{15 η^{4}}{11 π^{4}}) + \frac{3}{2} \frac{T}{m_{N}},

8-

Y_{e} = \frac{T^{3}}{(ρ / m_{N})} \frac{η}{3} (1 + \frac{η^{2}}{π^{2}}) .

9-

Y_{e} = {(k T / ℏ c)}^{3} (m_{N} / ρ) (η / 3) (1 + η^{2} / π^{2})

10-

v \frac{d Y_{e}}{d r} = λ_{ν_{e} n} + λ_{e^{+} n} - (λ_{ν_{e} n} + λ_{e^{+} n} + λ_{{\bar{ν}}_{e} p} + λ_{e^{-} p}) Y_{e},

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: hep-lat

Result: incorrect

Paper: https://arxiv.org/abs/1705.08653

Formulas:

1-

σ_{w}^{2} = w_{p} (t) σ_{p}^{2} (t) + w_{s} (t) σ_{s}^{2} (t) .

2-

w_{i} (t)

3-

σ_{i}^{2} (t)

4-

ℰ_{S} (X) = {𝐫 : S_{𝐫} \subset X},

5-

𝒟_{S} (X) = {𝐫 : S_{𝐫} \cap X \neq \emptyset},

6-

𝒪_{S} (X) = 𝒟_{S} (ℰ_{S} (X)) .

7-

[r, r + δ r]

8-

f (r) = \frac{Vol (𝒪_{S (r)} (X)) - Vol (𝒪_{S (r + δ r)} (X))}{Vol (X)},

9-

G_{α β} = \sum_{i} g_{α} (i) g_{β} (i),

10-

g_{α} (i)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0312281

Formulas:

1-

3 p \leftarrow 3 s

2-

3 p \leftarrow 3 s

3-

10^{- 2} ρ_{0}

4-

10^{- 3} ρ_{0}

5-

10^{- 4} ρ_{0}

6-

V_{H e - N a}

7-

ρ \sim ρ_{0} / 2

8-

ρ \sim ρ_{0} / 2

9-

S_{N a} = E (Na @ {He}_{N}) - E ({He}_{N})

10-

S_{N a} (N) = S_{0} + \frac{S_{1}}{N^{1 / 3}} + \frac{S_{2}}{N^{2 / 3}}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/1805.04664

Formulas:

1-

10^{- 6} - 10^{7}

2-

Φ_{ℓ} (t) = ⟨ P_{ℓ} (\cos θ (t)) ⟩,

3-

τ^{(1)} / τ^{(2)} = 3

4-

g_{1} (t)

5-

g_{1} (t) = ⟨ E_{s}^{*} (0) E_{s} (t) ⟩ / ⟨ {| E_{s} |}^{2} ⟩

6-

g_{2} (t) = ⟨ I (t) I (0) ⟩ / {⟨ I ⟩}^{2}

7-

g_{2} (t) = 1 + Λ C^{2} {| g_{1} (t) |}^{2} + 2 Λ C (1 - C) | g_{1} (t) |,

8-

g_{1} (t)

9-

1 - g_{1} (t_{0}) \approx 0.2

10-

g_{1} (t)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: gr-qc

Result: incorrect

Paper: https://arxiv.org/abs/1710.00038

Formulas:

1-

= i ω 𝐁,

2-

= - i ω 𝐃 + 𝐉_{free} .

3-

\exp (- i ω t)

4-

μ_{0}^{- 1} \nabla \times 𝐁

5-

= - i ω ϵ 𝐄 .

6-

\nabla \cdot ϵ_{0} 𝐄

7-

μ_{0}^{- 1} \nabla \times 𝐁

8-

= - i ω ϵ_{0} 𝐄 + 𝐉,

9-

ϵ 𝐄 = ϵ_{0} 𝐄 + 𝐏

10-

= - i ω 𝐏,

Formulas (html):

Correct Categorie: physics

Guessed Categorie: hep-th

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0202197

Formulas:

1-

f_{mol} = \frac{ρ (H_{2})}{ρ (HI) + ρ (H_{2})} = \frac{2 \times n (H_{2})}{n (HI) + 2 \times n (H_{2})} .

2-

(P, U, Z)

3-

C (HI) \times I (HI),

4-

n (H_{2})

5-

C (CO) \times I (CO),

6-

C (CO) = 1.1 \times 10^{20}

7-

Φ (R, ϕ) = Φ_{0} (R) + Φ_{1} (R, ϕ) .

8-

Φ_{0} (R) = - \frac{c^{2}}{a} \frac{1}{{(R^{2} + a^{2})}^{1 / 2}},

9-

c = v_{\max} (27 / 4) {}^{1 / 4}a

10-

Φ_{1} (R, ϕ) = ε \frac{a R^{2}}{{(R^{2} + a^{2})}^{3 / 2}} Φ_{0} (R) \cos 2 (ϕ - Ω_{p} t),

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0504456

Formulas:

1-

D (n - 1) - 4 = 0

2-

i ℏ u_{t}

3-

- \frac{ℏ^{2}}{2 m} \nabla^{2} u + [\frac{m}{2} (ω_{⟂}^{2} ρ^{2} + ω_{x}^{2} x^{2}) + V_{o p t} (x)] u

4-

+ g_{1} {| u |}^{2} u + g_{2} {| u |}^{4} u,

5-

V_{o p t} (x) = V_{0} \sin^{2} (k x)

6-

g_{1} = 4 π ℏ^{2} a_{s} / m

7-

u (r, t) = ϕ_{0} (ρ) ψ (x, t)

8-

ϕ_{0} = \sqrt{\frac{1}{π a_{⟂}^{2}}} \exp (- \frac{ρ^{2}}{2 a_{⟂}^{2}})

9-

- \frac{ℏ^{2}}{2 m} \nabla_{ρ}^{2} ϕ_{0} + \frac{m}{2} ω_{⟂}^{2} ρ^{2} ϕ_{0} = ℏ ω_{⟂} ϕ_{0} .

10-

i ℏ ψ_{t} = - \frac{ℏ^{2}}{2 m} ψ_{x x} + (\frac{m}{2} ω_{x}^{2} x^{2} + V_{0} \sin^{2} (k x)) ψ +

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: hep-lat

Result: incorrect

Paper: https://arxiv.org/abs/hep-ph/0411376

Formulas:

1-

χ^{0} χ^{0} \to γ γ

2-

χ^{0} χ^{0} \to γ Z

3-

\tilde{B} (κ_{1}^{'} h^{†} {\tilde{H}}_{1} + κ_{2}^{'} h {\tilde{H}}_{2}) + {\tilde{W}}^{a} (κ_{1} h^{†} τ^{a} {\tilde{H}}_{1} + κ_{2} {\tilde{H}}_{2} τ^{a} h) - λ {| h |}^{4} - μ {\tilde{H}}_{1} {\tilde{H}}_{2} - \frac{1}{2} (M_{1} \tilde{B} \tilde{B} + M_{2} \tilde{W} \tilde{W} + M_{3} \tilde{g} \tilde{g}) .

4-

𝐌_{χ^{𝟎}} = (\begin{matrix} M_{1} & 0 & - \frac{κ_{1}^{'} υ}{\sqrt{2}} & \frac{κ_{2}^{'} υ}{\sqrt{2}} \\ 0 & M_{2} & \frac{κ_{2} υ}{\sqrt{8}} & - \frac{κ_{1} υ}{\sqrt{8}} \\ - \frac{κ_{2}^{'} υ}{\sqrt{2}} & \frac{κ_{2} υ}{\sqrt{8}} & 0 & - μ \\ \frac{κ_{1}^{'} υ}{\sqrt{2}} & - \frac{κ_{1} υ}{\sqrt{8}} & - μ & 0 \end{matrix}),

5-

𝐌_{χ^{\pm}} = (\begin{matrix} M_{2} & \frac{κ_{1} υ}{2} \\ \frac{κ_{2} υ}{2} & μ \end{matrix}),

6-

κ_{1}^{'} = \sqrt{\frac{3}{10}} g_{1} \sin β κ_{2}^{'} = \sqrt{\frac{3}{10}} g_{1} \cos β κ_{1} = \sqrt{2} g_{2} \sin β κ_{2} = \sqrt{2} g_{2} \cos β λ = \frac{\frac{3}{5} g_{1}^{2} + g_{2}^{2}}{8} \cos^{2} 2 β .

7-

χ^{0} χ^{0} \to h \to W W^{*}

8-

χ^{0} χ^{0} \to h \to W W^{*}

9-

h \to W W^{*} \to W f \bar{f}

10-

ρ (r) = \frac{ρ_{0}}{(1 + \frac{r}{R}) (1 + \frac{r^{2}}{R^{2}})}

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/0909.3072

Formulas:

1-

S U (3)

2-

s u (4)

3-

| Φ_{B C S} ⟩

4-

S U (3)

5-

\tilde{Δ} = (Δ_{1}, Δ_{2}, Δ_{3})

6-

Δ_{1} = Δ_{2} = Δ_{3} = Δ

7-

Δ_{1} = \sqrt{3} Δ

8-

Δ_{2} = Δ_{3} = 0

9-

⟨ Φ_{B C S} | S_{Λ_{k}} | Φ_{B C S} ⟩ = 0, k = 1, \dots, 8,

10-

S U (3)

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: cs

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0310476

Formulas:

1-

= 1010_{- 265}^{+ 295}

2-

N_{O viii} > 3.4 \times 10^{16} {cm}^{- 2}

3-

< 19 h_{70}^{- 1}

4-

10^{5} K < T < 10^{7} K

5-

\sim 0.46 - 0.49 ″

6-

1.23 \times 10^{21} {cm}^{- 2}

7-

τ = {0.06}_{- 0.05}^{+ 0.05}

8-

= 1010_{- 265}^{+ 295}

9-

= {2.17}_{- 0.63}^{+ 0.57}

10-

Δ v = - 5500 \pm 140

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/1502.05358

Formulas:

1-

δ 𝑿 (𝒙_{0}, t, τ) = 𝑿 (𝒙_{0}, t) - 𝑿 (𝒙_{0}, t - τ)

2-

𝑿 (𝒙_{0}, t)

3-

d 𝑿 / d t = 𝐮

4-

Θ (t, τ)

5-

\cos (Θ (t, τ)) = \frac{δ 𝑿 (𝒙_{0}, t, τ) \cdot δ 𝑿 (𝒙_{0}, t + τ, τ)}{| δ 𝑿 (𝒙_{0}, t, τ) | | δ 𝑿 (𝒙_{0}, t + τ, τ) |} .

6-

θ (τ) \equiv ⟨ | Θ (t, τ) | ⟩ .

7-

Θ (τ, t)

8-

κ (t) = lim_{τ \to 0} \frac{| Θ (t, τ) |}{2 τ ∥ 𝒖 (t) ∥},

9-

\tilde{θ} (τ) \equiv θ (τ) σ_{u} / {(ϵ τ)}^{1 / 2}

10-

τ_{K} = {(ν / ϵ)}^{1 / 2} = 0.036

Formulas (html):

Correct Categorie: physics

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/1103.3576

Formulas:

1-

(x, y) \to (x - t, y)

2-

(x, y) \to (x, y - t)

3-

(x, y) \to (x - s, y - t)

4-

∣ s - t ∣ < k

5-

x - s \geq 0, y - t \geq 0

6-

π = 3, 14 \dots

7-

k = ⌊ π ⌋ = 3

8-

α = π / (π - 1)

9-

(⌊ n α ⌋)

10-

(⌊ n π ⌋)

Formulas (html):

Correct Categorie: math

Guessed Categorie: cs

Result: incorrect

Paper: https://arxiv.org/abs/1904.08768

Formulas:

1-

100 - 550 M P a

2-

850 - 1050^{\circ} C

3-

f_{i j}^{p a r t i c l e} = {\begin{matrix} \frac{1}{2} \frac{χ_{A P B}}{∥ 𝐛 ∥} ∥ 𝐥_{i j} ∥ \tanh (\frac{3 (L - d_{m i n})}{L}) 𝐧^{𝐬} & d_{m i n} \leq L \\ 0 & d_{m i n} > L \end{matrix}

4-

f_{i j}^{p a r t i c l e}

5-

χ_{A P B}

6-

d_{m i n}

7-

B_{i j} (ξ) = {\begin{matrix} B^{g} m_{i} m_{j} + B^{c} n_{i} n_{j} + B^{l} t_{i} t_{j}, & \forall 𝐧 \in {111} \\ B^{c} δ_{i j} + (B^{g} - B^{l}) t_{i} t_{j}, & \forall 𝐧 \notin {111} \end{matrix}

8-

B_{i j} (ξ)

9-

m_{i} = ϵ_{i j k} n_{j} t_{k}

10-

ϵ_{i j k}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: hep-th

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0409140

Formulas:

1-

10^{17} e V

2-

J (E_{i}) = N (E_{i}) * \frac{1}{Δ E} * \frac{1}{\frac{R_{M C} (E_{i})}{G_{M C} (E_{i})} * A Ω * t}

3-

N (E_{i})

4-

10^{18.5} e V

5-

10^{17.6} e V

6-

X_{m a x}

7-

X_{m a x}

8-

10^{18} e V

9-

> 10^{19.5} e V

10-

10^{19.55} e V

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/2009.01914

Formulas:

1-

T_{*} = \frac{π}{2} \frac{R_{z} (r)}{r} {[\frac{H (r)}{r}]}^{2},

2-

\nabla_{ν} T_{μ}^{ν} = - ℒ u_{μ},

3-

Θ_{top} (r, ϕ)

4-

Θ_{bot} (r, ϕ)

5-

\int_{0}^{Θ_{top} (r, ϕ)} κ ρ (r, ϕ) 𝑑 θ \sqrt{g_{θ θ}} = 1,

6-

- \int_{π}^{Θ_{bot} (r, ϕ)} κ ρ (r, ϕ) 𝑑 θ \sqrt{g_{θ θ}} = 1,

7-

0.4 {cm}^{2} g^{- 1}

8-

(r, θ, ϕ)

9-

Θ_{top} < θ < Θ_{bot}

10-

\dot{M} / {\dot{M}}_{Edd}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0104328

Formulas:

1-

\cot (θ_{H})

2-

\cot (θ_{H})

3-

R_{H} (T)

4-

\cot (θ_{H}) = ρ_{x x} / ρ_{x y}

5-

R_{H}^{- 1} (T)

6-

ρ_{x x} (T)

7-

τ_{t r}^{- 1}

8-

R_{H}^{- 1} = \cot (θ_{H}) \cdot H / ρ_{x x} \sim τ_{H}^{- 1} / τ_{t r}^{- 1}

9-

\cot (θ_{H}) = A T^{2} + C

10-

A r + O_{2}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1005.2652

Formulas:

1-

\tilde{S} = \sum_{s < s_{m a x}} \frac{n_{s} s^{2}}{N},

2-

R_{i j} = R_{j i} = \frac{∥ \vec{X_{i}} \cdot \vec{X_{j}} ∥}{∥ \vec{X_{i}} ∥ ∥ \vec{X_{j}} ∥} .

3-

B_{E} = \frac{\sqrt{S_{x} S_{y}}}{S_{E}},

4-

S_{E} = S_{E^{'}} = S_{E^{''}} = 3

5-

\tilde{S} (f)

6-

J_{E} = \frac{| U_{x} \cap U_{y} |}{| U_{x} \cup U_{y} |},

7-

D_{E} = k_{x} k_{y},

8-

{(k_{x} k_{y})}^{α}

9-

C_{E} = \sum_{s \neq t} \frac{σ_{s t} (E)}{σ_{s t}},

10-

σ_{s t} (E)

Formulas (html):

Correct Categorie: physics

Guessed Categorie: hep-lat

Result: incorrect

Paper: https://arxiv.org/abs/1109.1858

Formulas:

1-

C (V) = e d n / d V

2-

ν (V) = n (V) / N

3-

ν (V) = n (V) / N

4-

V_{k} = k e / C

5-

e V_{k} = E_{v = k} - E_{v = k - 1}

6-

r = (\sqrt{2} - 1) b ≃ 0.41 b

7-

r = (\sqrt{6} / 2 - 1) b ≃ 0.22 b

8-

a_{B} = ℏ^{2} ϵ / m e^{2}

9-

ψ (r) = \sqrt{\frac{1}{2 π a}} \frac{\sin (π r / a)}{r}

10-

E_{q} = \frac{ℏ^{2} π^{2}}{2 m a^{2}} .

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/0810.4687

Formulas:

1-

M_{C r / F e}

2-

_{C r / F e}

3-

_{C r / F e}

4-

M_{C r / F e}

5-

M_{C r / F e}

6-

M_{C r / F e}

7-

M_{C r / F e}

8-

M_{C r / F e}

9-

M_{C r / F e}

10-

M_{C r / F e}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/1109.3762

Formulas:

1-

(0.5 - 1) \sim 10^{8} M_{⊙}

2-

Δ χ^{2} = 10

3-

{1.57}_{- 0.97}^{+ 0.70} \times 10^{- 5}

4-

c o s θ = 0.5

5-

Δ χ^{2} = 35

6-

(2.7 \pm 1.1) \times 10^{23}

7-

(2.3 \pm 0.2) \times 10^{- 4}

8-

(2.7 - 2.9) \times 10^{- 4}

9-

Δ χ^{2} = 36

10-

N_{H} = 2.6 \times 10^{24}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0501404

Formulas:

1-

ρ / \bar{ρ} > 100

2-

0.5 < ρ / \bar{ρ} < 5

3-

0.5 < ρ / \bar{ρ} < 5

4-

0.015 < Ω_{b} h^{2} < 0.021

5-

Ω_{b} = 0.0224 \pm 0.0009

6-

Ω_{m} = {0.135}_{- 0.009}^{+ 0.008}

7-

f_{c} \equiv Ω_{b} / Ω_{m} = {0.166}_{- 0.013}^{+ 0.012}

8-

f_{b} (𝐱)

9-

f_{b} (𝐱)

10-

f_{b} (𝐱)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/9907283

Formulas:

1-

ε = E / Δ x = \sqrt{⟨ {(\frac{d ε}{d X})}^{2} ⟩} X,

2-

(\nabla^{2} - k^{2}) (\nabla^{2} + k^{2}) W = 0,

3-

f = \frac{k^{2}}{2 π} \sqrt{\frac{E_{Y} h^{3}}{12 ρ (1 - ν^{2})}},

4-

(\nabla^{2} + k^{2}) W_{1} = 0 and (\nabla^{2} - k^{2}) W_{2} = 0 .

5-

Δ_{3} (L)

6-

\tilde{c} (w, x)

7-

Δ_{3} (L)

8-

v (x) = ⟨ {(n (ε, x^{'}) - n (ε, x^{'} + x))}^{2} ⟩,

9-

n (ε, x)

10-

\tilde{c} (ω, x)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0304233

Formulas:

1-

U_{C} ≲ Γ ≲ Δ E

2-

Δ E ≪ U_{C}

3-

Δ E / U_{C} \sim 2

4-

d I / d V_{s d}

5-

U_{C} = e^{2} / C_{Σ}

6-

C_{g} / C_{Σ} = 0.0036

7-

C_{s} / C_{d} = 0.45

8-

V_{s d} = 0

9-

Γ_{s (d)} = 2 π {| t_{s (d)} |}^{2} N_{0}

10-

t_{s (d)}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/1306.3259

Formulas:

1-

11' \times 9'

2-

55 ″ \times 55 ″

3-

18^{h} 20^{m} {25.1}^{s}

4-

- 16^{\circ} 13^{'} {02.1}^{''}

5-

4^{'} 25^{''} \times 2^{'} 45^{''}

6-

p \geq 3 σ_{p}

7-

2 σ_{p} \leq p \leq 3 σ_{p}

8-

18^{h} 20^{m} 25^{s}

9-

- 16 ° 13' 02 ″

10-

p \geq 3 σ_{p}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/2012.08342

Formulas:

1-

t \bar{t} W^{+}

2-

t \bar{t} H

3-

t \bar{t} W

4-

t \bar{t} W

5-

t \bar{t} W

6-

t \bar{t} W^{+}

7-

pp \to e^{+} ν_{e} μ^{-} {\bar{ν}}_{μ} τ^{+} ν_{τ} b \bar{b}

8-

𝒪 (α_{s}^{2} α^{6})

9-

𝒪 (α_{s}^{3} α^{6})

10-

g q / g \bar{q}

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1311.3197

Formulas:

1-

ℋ = - J_{b} \sum_{b u l k} δ (s_{x, y} - s_{x^{'}, y^{'}}) - J_{s} \sum_{s u r f a c e} δ (s_{x, y_{s}} - s_{x^{'}, y_{s}}),

2-

δ (x) = 1

3-

δ (x) = 0

4-

J_{s} = J_{b} = J

5-

J / k_{B} = 1

6-

s_{x, y} = 1, \dots, q

7-

C_{s s} (x)

8-

C_{s b} (y)

9-

m (y) = (q N_{m} (y) / L - 1) / (q - 1)

10-

N_{m} (y)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: math

Result: incorrect

Paper: https://arxiv.org/abs/1303.0834

Formulas:

1-

M = 4.70 \pm 0.14 \times 10^{8} M_{⊙}

2-

M = {4.5}_{- 3.0}^{+ 4.2} \times 10^{8} M_{⊙}

3-

5.75 \times 10^{8} M_{⊙}

4-

4.70 \pm 1.05 \times 10^{8} M_{⊙}

5-

4.5 \times 10^{8} M_{⊙}

6-

dof = 68 - 2 = 66

7-

χ_{\min}^{2} / dof = 1.27

8-

χ^{2} / dof = χ^{2} / 68

9-

(4.70 - 4.50) / 1.05 = 0.19

10-

χ_{\min}^{2} / dof = 83.91 / 66 = 1.27

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: hep-th

Result: incorrect

Paper: https://arxiv.org/abs/1303.5011

Formulas:

1-

σ (ω) = σ_{1} (ω) + i σ_{2} (ω) = \frac{σ_{0}}{(1 - i ω / Γ)},

2-

σ_{1} (ω)

3-

σ_{2} (ω)

4-

m^{*} / m = Γ / Γ^{*}

5-

Γ (ω) = \frac{ω_{p}^{2}}{4 π} Re {\frac{1}{σ (ω)}} = \frac{ω_{p}^{2}}{4 π} \frac{σ_{1} (ω)}{{| σ (ω) |}^{2}} = \frac{ω_{p}^{2}}{4 π} ρ_{1} (ω),

6-

ω_{p} = \sqrt{4 π n e^{2} / m}

7-

Γ (ω) \propto ρ_{1} (ω)

8-

ρ_{1} = Re (1 / σ)

9-

Γ (T, ω) = Γ_{0} + a {(k_{B} T)}^{2} + b {(ℏ ω)}^{2}

10-

a / b = 4 π^{2}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/nucl-ex/0412041

Formulas:

1-

\sqrt{s_{N N}} = 200

2-

T_{c} \sim 150 - 180 M e V

3-

\sqrt{s_{N N}} = 200

4-

Ω^{-} + {\bar{Ω}}^{+}

5-

N_{p a r t}

6-

N_{p a r t}

7-

N_{b i n}

8-

N_{p a r t}

9-

N_{p a r t}

10-

N_{p a r t}

Formulas (html):

Correct Categorie: nucl-ex

Guessed Categorie: cs

Result: incorrect

Paper: https://arxiv.org/abs/2009.13739

Formulas:

1-

H_{0} = 74.03 \pm 1.42

2-

H_{0} = 67.4 \pm 0.5

3-

n_{AGN} \approx 2 \times 10^{- 5}

4-

p (d_{L} | {\hat{d}}_{L}, σ_{d_{L}}^{2}) = \frac{1}{\sqrt{2 π σ_{d_{L}}^{2}} {\hat{d}}_{L}} \exp [- \frac{{(\log d_{L} - \log {\hat{d}}_{L})}^{2}}{2 σ_{d_{L}}^{2}}]

5-

d_{L} = \frac{c (1 + z)}{H_{0}} \int_{0}^{z} \frac{d z^{'}}{E (z^{'})}

6-

E (z) = \sqrt{Ω_{r} {(1 + z)}^{4} + Ω_{m} {(1 + z)}^{3} + Ω_{k} {(1 + z)}^{2} + Ω_{Λ}} .

7-

{H_{0}, Ω_{r}, Ω_{m}, Ω_{k}, Ω_{Λ}} = {67.8 km s^{- 1} {Mpc}^{- 1}, 0, 0.306, 0, 0.694}

8-

{\hat{H}}_{0} / H_{0} = d_{L} / {\hat{d}}_{L}

9-

{{\hat{H}}_{0, 1}, {\hat{H}}_{0, 2}, \dots, {\hat{H}}_{0, N}}

10-

σ (\hat{H_{0}}) \propto N^{- 1 / 2}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1010.3728

Formulas:

1-

z_{a b s}

2-

M_{B H} = 5.5 {FWHM}^{2} R_{b l r} / G

3-

R_{b l r}

4-

\log_{10} R_{b l r} = - {21.3}_{- 2.8}^{+ 2.9} + {0.519}_{- 0.066}^{+ 0.063} \log_{10} (λ L_{λ} (5100))

5-

R_{b l r}

6-

L_{λ} (5100)

7-

f_{λ} (5100) = 1.5 \times 10^{- 16}

8-

λ L_{λ} (5100) = 2.66 \times 10^{45}

9-

R_{b l r} = 190

10-

M_{B H} = 3.4 \times 10^{9}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/0708.0434

Formulas:

1-

e t a l .

2-

S i O_{2}

3-

F = \frac{ℏ c}{2 π^{2}} \int_{0}^{\infty} Q 𝑑 Q \int_{q > 0} 𝑑 k \frac{k^{2}}{q} (G^{s} + G^{p}),

4-

G_{s} = {(r_{1 s}^{- 1} r_{2 s}^{- 1} \exp (- 2 k L) - 1)}^{- 1}

5-

G_{p} = {(r_{1 s}^{- 1} r_{2 s}^{- 1} \exp (- 2 k L) - 1)}^{- 1}

6-

k = \sqrt{q^{2} + Q^{2}}

7-

| r_{p} | = | r_{s} | = 1

8-

F_{c} = - \frac{ℏ c π^{2}}{240 L^{4}} .

9-

r_{p, s} = \frac{r_{p s}^{01} + r_{p s}^{12} e^{- 2 δ}}{1 + r_{p s}^{01} r_{p s}^{12} e^{- 2 δ}}

10-

r_{p, s}^{i, j}

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/0711.0842

Formulas:

1-

μ_{α a b s}

2-

μ_{δ a b s}

3-

π_{a b s}

4-

12^{h} 07^{m} {33.460}^{s}

5-

- 39 ° 32' 53.97 ″

6-

(5.5' \times 5.5')

7-

Δ F = - 0.004 \pm 0.001

8-

σ_{d c r} = σ_{Δ F} < Z_{a} > = 0.38

9-

< Z_{a} > = 11.8 °

10-

Δ π = + 0.58 \pm 0.01

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/1908.06833

Formulas:

1-

{x^{i} ∣ i = 0, 1, 2, \dots}

2-

{x^{i} ∣ i = 0, 1, 2, \dots}

3-

δ (a b) = σ (a) δ (b) + δ (a) b

4-

x a = σ (a) x + δ (a)

5-

F (x) \in ℛ

6-

σ : 𝔽 ⟶ 𝔽^{n \times n}

7-

δ : 𝔽 ⟶ 𝔽^{n}

8-

σ : 𝔽 ⟶ 𝔽^{n \times n}

9-

σ = diag (σ_{1}, σ_{2}, \dots, σ_{n})

10-

σ = diag (σ_{1}, σ_{2}, \dots, σ_{n})

Formulas (html):

Correct Categorie: math

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/1410.2571

Formulas:

1-

A_{s} = 2.215 \times 10^{- 9}

2-

P (k) = A_{s} {(\frac{k}{k_{p}})}^{n_{s} - 1 + \frac{1}{2} α_{s} \ln (k / k_{p})},

3-

n_{s} = 0.9603 \pm 0.0073

4-

α_{s} = - 0.0134 \pm 0.0090

5-

- 0.046 < α_{s} < - 0.003

6-

k \sim 0.13 {Mpc}^{- 1}

7-

C_{ℓ}^{𝐭𝐡} = 4 π \int_{0}^{\infty} d \ln k Δ_{ℓ}^{2} (k) P (k),

8-

ℓ \sim 180^{o} / θ

9-

Δ_{ℓ} (k)

10-

T (p) = T_{CMB} [1 + Θ (p)]

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: gr-qc

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0203385

Formulas:

1-

σ (θ, ϕ)

2-

Y_{l, m} (θ, ϕ)

3-

σ (θ, ϕ) = \sum_{l = 0}^{\infty} \sum_{m = - l}^{+ l} A_{l, m} Y_{l, m} (θ, ϕ)

4-

(θ_{i}, ϕ_{i})

5-

A_{l, m} = \sum_{i = 1}^{N} Y_{l, m}^{*} (θ_{i}, ϕ_{i})

6-

χ_{r e d}^{2} \sim 1

7-

χ_{r e d}^{2}

8-

θ = 97.2 \pm {0.1}^{o}, ϕ = 168.0 \pm {0.1}^{o}

9-

Δ δ = 0.5 \times 10^{- 2}

10-

S (ν) \propto ν^{- α}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: physics

Result: incorrect

Paper: https://arxiv.org/abs/1001.3961

Formulas:

1-

| L ⟩, | M ⟩

2-

H = (\begin{matrix} 0 & J_{L M} & 0 \\ J_{L M} & 0 & J_{M R} \\ 0 & J_{M R} & 0 \end{matrix}) .

3-

| D ⟩ = \cos θ | L ⟩ + \sin θ | R ⟩ .

4-

\tan θ = J_{M R} / J_{L M}

5-

V = {\begin{matrix} \frac{1}{2 m} ω^{2} {(x + \frac{d}{2})}^{2} & for x \leq 0 \\ \frac{1}{2 m} ω^{2} {(x - \frac{d}{2})}^{2} & for x \geq 0 . \end{matrix}

6-

ψ_{1} (x)

7-

= N_{1} D_{ν} [- \frac{2 m ω}{ℏ} (x + \frac{d}{2})]

8-

for x \leq 0,

9-

ψ_{2} (x)

10-

= N_{2} D_{ν} [\frac{2 m ω}{ℏ} (x - \frac{d}{2})]

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: hep-th

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/9611100

Formulas:

1-

0.1 \leq Ω_{ν} \leq 0.5

2-

0.3 \leq Ω_{0} \leq 0.5

3-

0.18 \sim < Γ \sim < 0.25

4-

20 h^{- 1} Mpc

5-

- 1.1 \sim < n_{eff} \sim < - 0.9

6-

0.2 \sim < Ω_{ν} \sim < 0.3

7-

0.3 \sim < Ω_{0} \sim < 0.5

8-

z \sim < 5

9-

\sim 10^{11} M_{⊙}

10-

P (k) \propto k

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: hep-ph

Result: incorrect

Paper: https://arxiv.org/abs/0709.0906

Formulas:

1-

z = 28 t_{1} + 14 t_{2} + 4 t_{3} + t_{4}

2-

H_{m a x}

3-

R (I, i, n)

4-

C (t, i)

5-

S (x_{i}, x_{j}) = 1

6-

c o s t (I)

7-

m i n t e c (I)

8-

(P_{1} (I))

9-

(P_{1} (I)) {\begin{matrix} Minimize \sum_{t \in Ω_{t}} x_{t} subject to, \\ \sum_{t / C (t, i) \geq n, t \in Ω_{t}} x_{t} \geq R (I, i, n) \forall i, n, \\ x_{t} \in {0, 1} t \in Ω_{t} \end{matrix}

10-

w_{I} = m i n t e c (I) \times T (I)

Formulas (html):

<math><mrow id="S1.p1.1.m1.1.1" xref="S1.p1.1.m1.1.1.cmml"><mi id="S1.p1.1.m1.1.1.2" xref="S1.p1.1.m1.1.1.2.cmml">z</mi><mo id="S1.p1.1.m1.1.1.1" xref="S1.p1.1.m1.1.1.1.cmml">=</mo><mrow id="S1.p1.1.m1.1.1.3" xref="S1.p1.1.m1.1.1.3.cmml"><mrow id="S1.p1.1.m1.1.1.3.2" xref="S1.p1.1.m1.1.1.3.2.cmml"><mn id="S1.p1.1.m1.1.1.3.2.2" xref="S1.p1.1.m1.1.1.3.2.2.cmml">28</mn><mo id="S1.p1.1.m1.1.1.3.2.1" xref="S1.p1.1.m1.1.1.3.2.1.cmml">⁢</mo><msub id="S1.p1.1.m1.1.1.3.2.3" xref="S1.p1.1.m1.1.1.3.2.3.cmml"><mi id="S1.p1.1.m1.1.1.3.2.3.2" xref="S1.p1.1.m1.1.1.3.2.3.2.cmml">t</mi><mn id="S1.p1.1.m1.1.1.3.2.3.3" xref="S1.p1.1.m1.1.1.3.2.3.3.cmml">1</mn></msub></mrow><mo id="S1.p1.1.m1.1.1.3.1" xref="S1.p1.1.m1.1.1.3.1.cmml">+</mo><mrow id="S1.p1.1.m1.1.1.3.3" xref="S1.p1.1.m1.1.1.3.3.cmml"><mn id="S1.p1.1.m1.1.1.3.3.2" xref="S1.p1.1.m1.1.1.3.3.2.cmml">14</mn><mo id="S1.p1.1.m1.1.1.3.3.1" xref="S1.p1.1.m1.1.1.3.3.1.cmml">⁢</mo><msub id="S1.p1.1.m1.1.1.3.3.3" xref="S1.p1.1.m1.1.1.3.3.3.cmml"><mi id="S1.p1.1.m1.1.1.3.3.3.2" xref="S1.p1.1.m1.1.1.3.3.3.2.cmml">t</mi><mn id="S1.p1.1.m1.1.1.3.3.3.3" xref="S1.p1.1.m1.1.1.3.3.3.3.cmml">2</mn></msub></mrow><mo id="S1.p1.1.m1.1.1.3.1a" xref="S1.p1.1.m1.1.1.3.1.cmml">+</mo><mrow id="S1.p1.1.m1.1.1.3.4" xref="S1.p1.1.m1.1.1.3.4.cmml"><mn id="S1.p1.1.m1.1.1.3.4.2" xref="S1.p1.1.m1.1.1.3.4.2.cmml">4</mn><mo id="S1.p1.1.m1.1.1.3.4.1" xref="S1.p1.1.m1.1.1.3.4.1.cmml">⁢</mo><msub id="S1.p1.1.m1.1.1.3.4.3" xref="S1.p1.1.m1.1.1.3.4.3.cmml"><mi id="S1.p1.1.m1.1.1.3.4.3.2" xref="S1.p1.1.m1.1.1.3.4.3.2.cmml">t</mi><mn id="S1.p1.1.m1.1.1.3.4.3.3" xref="S1.p1.1.m1.1.1.3.4.3.3.cmml">3</mn></msub></mrow><mo id="S1.p1.1.m1.1.1.3.1b" xref="S1.p1.1.m1.1.1.3.1.cmml">+</mo><msub id="S1.p1.1.m1.1.1.3.5" xref="S1.p1.1.m1.1.1.3.5.cmml"><mi id="S1.p1.1.m1.1.1.3.5.2" xref="S1.p1.1.m1.1.1.3.5.2.cmml">t</mi><mn id="S1.p1.1.m1.1.1.3.5.3" xref="S1.p1.1.m1.1.1.3.5.3.cmml">4</mn></msub></mrow></mrow></math>, <math><msub id="S1.p1.4.m4.1.1" xref="S1.p1.4.m4.1.1.cmml"><mi id="S1.p1.4.m4.1.1.2" xref="S1.p1.4.m4.1.1.2.cmml">H</mi><mrow id="S1.p1.4.m4.1.1.3" xref="S1.p1.4.m4.1.1.3.cmml"><mi id="S1.p1.4.m4.1.1.3.2" xref="S1.p1.4.m4.1.1.3.2.cmml">m</mi><mo id="S1.p1.4.m4.1.1.3.1" xref="S1.p1.4.m4.1.1.3.1.cmml">⁢</mo><mi id="S1.p1.4.m4.1.1.3.3" xref="S1.p1.4.m4.1.1.3.3.cmml">a</mi><mo id="S1.p1.4.m4.1.1.3.1a" xref="S1.p1.4.m4.1.1.3.1.cmml">⁢</mo><mi id="S1.p1.4.m4.1.1.3.4" xref="S1.p1.4.m4.1.1.3.4.cmml">x</mi></mrow></msub></math>, <math><mrow id="S2.p1.3.m3.3.4" xref="S2.p1.3.m3.3.4.cmml"><mi id="S2.p1.3.m3.3.4.2" xref="S2.p1.3.m3.3.4.2.cmml">R</mi><mo id="S2.p1.3.m3.3.4.1" xref="S2.p1.3.m3.3.4.1.cmml">⁢</mo><mrow id="S2.p1.3.m3.3.4.3.2" xref="S2.p1.3.m3.3.4.3.1.cmml"><mo stretchy="false" id="S2.p1.3.m3.3.4.3.2.1" xref="S2.p1.3.m3.3.4.3.1.cmml">(</mo><mi id="S2.p1.3.m3.1.1" xref="S2.p1.3.m3.1.1.cmml">I</mi><mo id="S2.p1.3.m3.3.4.3.2.2" xref="S2.p1.3.m3.3.4.3.1.cmml">,</mo><mi id="S2.p1.3.m3.2.2" xref="S2.p1.3.m3.2.2.cmml">i</mi><mo id="S2.p1.3.m3.3.4.3.2.3" xref="S2.p1.3.m3.3.4.3.1.cmml">,</mo><mi id="S2.p1.3.m3.3.3" xref="S2.p1.3.m3.3.3.cmml">n</mi><mo stretchy="false" id="S2.p1.3.m3.3.4.3.2.4" xref="S2.p1.3.m3.3.4.3.1.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S2.p1.7.m7.2.3" xref="S2.p1.7.m7.2.3.cmml"><mi id="S2.p1.7.m7.2.3.2" xref="S2.p1.7.m7.2.3.2.cmml">C</mi><mo id="S2.p1.7.m7.2.3.1" xref="S2.p1.7.m7.2.3.1.cmml">⁢</mo><mrow id="S2.p1.7.m7.2.3.3.2" xref="S2.p1.7.m7.2.3.3.1.cmml"><mo stretchy="false" id="S2.p1.7.m7.2.3.3.2.1" xref="S2.p1.7.m7.2.3.3.1.cmml">(</mo><mi id="S2.p1.7.m7.1.1" xref="S2.p1.7.m7.1.1.cmml">t</mi><mo id="S2.p1.7.m7.2.3.3.2.2" xref="S2.p1.7.m7.2.3.3.1.cmml">,</mo><mi id="S2.p1.7.m7.2.2" xref="S2.p1.7.m7.2.2.cmml">i</mi><mo stretchy="false" id="S2.p1.7.m7.2.3.3.2.3" xref="S2.p1.7.m7.2.3.3.1.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S2.p1.10.m10.2.2" xref="S2.p1.10.m10.2.2.cmml"><mrow id="S2.p1.10.m10.2.2.2" xref="S2.p1.10.m10.2.2.2.cmml"><mi id="S2.p1.10.m10.2.2.2.4" xref="S2.p1.10.m10.2.2.2.4.cmml">S</mi><mo id="S2.p1.10.m10.2.2.2.3" xref="S2.p1.10.m10.2.2.2.3.cmml">⁢</mo><mrow id="S2.p1.10.m10.2.2.2.2.2" xref="S2.p1.10.m10.2.2.2.2.3.cmml"><mo stretchy="false" id="S2.p1.10.m10.2.2.2.2.2.3" xref="S2.p1.10.m10.2.2.2.2.3.cmml">(</mo><msub id="S2.p1.10.m10.1.1.1.1.1.1" xref="S2.p1.10.m10.1.1.1.1.1.1.cmml"><mi id="S2.p1.10.m10.1.1.1.1.1.1.2" xref="S2.p1.10.m10.1.1.1.1.1.1.2.cmml">x</mi><mi id="S2.p1.10.m10.1.1.1.1.1.1.3" xref="S2.p1.10.m10.1.1.1.1.1.1.3.cmml">i</mi></msub><mo id="S2.p1.10.m10.2.2.2.2.2.4" xref="S2.p1.10.m10.2.2.2.2.3.cmml">,</mo><msub id="S2.p1.10.m10.2.2.2.2.2.2" xref="S2.p1.10.m10.2.2.2.2.2.2.cmml"><mi id="S2.p1.10.m10.2.2.2.2.2.2.2" xref="S2.p1.10.m10.2.2.2.2.2.2.2.cmml">x</mi><mi id="S2.p1.10.m10.2.2.2.2.2.2.3" xref="S2.p1.10.m10.2.2.2.2.2.2.3.cmml">j</mi></msub><mo stretchy="false" id="S2.p1.10.m10.2.2.2.2.2.5" xref="S2.p1.10.m10.2.2.2.2.3.cmml">)</mo></mrow></mrow><mo id="S2.p1.10.m10.2.2.3" xref="S2.p1.10.m10.2.2.3.cmml">=</mo><mn id="S2.p1.10.m10.2.2.4" xref="S2.p1.10.m10.2.2.4.cmml">1</mn></mrow></math>, <math><mrow id="S2.p1.16.m16.1.2" xref="S2.p1.16.m16.1.2.cmml"><mi id="S2.p1.16.m16.1.2.2" xref="S2.p1.16.m16.1.2.2.cmml">c</mi><mo id="S2.p1.16.m16.1.2.1" xref="S2.p1.16.m16.1.2.1.cmml">⁢</mo><mi id="S2.p1.16.m16.1.2.3" xref="S2.p1.16.m16.1.2.3.cmml">o</mi><mo id="S2.p1.16.m16.1.2.1a" xref="S2.p1.16.m16.1.2.1.cmml">⁢</mo><mi id="S2.p1.16.m16.1.2.4" xref="S2.p1.16.m16.1.2.4.cmml">s</mi><mo id="S2.p1.16.m16.1.2.1b" xref="S2.p1.16.m16.1.2.1.cmml">⁢</mo><mi id="S2.p1.16.m16.1.2.5" xref="S2.p1.16.m16.1.2.5.cmml">t</mi><mo id="S2.p1.16.m16.1.2.1c" xref="S2.p1.16.m16.1.2.1.cmml">⁢</mo><mrow id="S2.p1.16.m16.1.2.6.2" xref="S2.p1.16.m16.1.2.cmml"><mo stretchy="false" id="S2.p1.16.m16.1.2.6.2.1" xref="S2.p1.16.m16.1.2.cmml">(</mo><mi id="S2.p1.16.m16.1.1" xref="S2.p1.16.m16.1.1.cmml">I</mi><mo stretchy="false" id="S2.p1.16.m16.1.2.6.2.2" xref="S2.p1.16.m16.1.2.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S2.SS1.p1.2.m2.1.2" xref="S2.SS1.p1.2.m2.1.2.cmml"><mi id="S2.SS1.p1.2.m2.1.2.2" xref="S2.SS1.p1.2.m2.1.2.2.cmml">m</mi><mo id="S2.SS1.p1.2.m2.1.2.1" xref="S2.SS1.p1.2.m2.1.2.1.cmml">⁢</mo><mi id="S2.SS1.p1.2.m2.1.2.3" xref="S2.SS1.p1.2.m2.1.2.3.cmml">i</mi><mo id="S2.SS1.p1.2.m2.1.2.1a" xref="S2.SS1.p1.2.m2.1.2.1.cmml">⁢</mo><mi id="S2.SS1.p1.2.m2.1.2.4" xref="S2.SS1.p1.2.m2.1.2.4.cmml">n</mi><mo id="S2.SS1.p1.2.m2.1.2.1b" xref="S2.SS1.p1.2.m2.1.2.1.cmml">⁢</mo><mi id="S2.SS1.p1.2.m2.1.2.5" xref="S2.SS1.p1.2.m2.1.2.5.cmml">t</mi><mo id="S2.SS1.p1.2.m2.1.2.1c" xref="S2.SS1.p1.2.m2.1.2.1.cmml">⁢</mo><mi id="S2.SS1.p1.2.m2.1.2.6" xref="S2.SS1.p1.2.m2.1.2.6.cmml">e</mi><mo id="S2.SS1.p1.2.m2.1.2.1d" xref="S2.SS1.p1.2.m2.1.2.1.cmml">⁢</mo><mi id="S2.SS1.p1.2.m2.1.2.7" xref="S2.SS1.p1.2.m2.1.2.7.cmml">c</mi><mo id="S2.SS1.p1.2.m2.1.2.1e" xref="S2.SS1.p1.2.m2.1.2.1.cmml">⁢</mo><mrow id="S2.SS1.p1.2.m2.1.2.8.2" xref="S2.SS1.p1.2.m2.1.2.cmml"><mo stretchy="false" id="S2.SS1.p1.2.m2.1.2.8.2.1" xref="S2.SS1.p1.2.m2.1.2.cmml">(</mo><mi id="S2.SS1.p1.2.m2.1.1" xref="S2.SS1.p1.2.m2.1.1.cmml">I</mi><mo stretchy="false" id="S2.SS1.p1.2.m2.1.2.8.2.2" xref="S2.SS1.p1.2.m2.1.2.cmml">)</mo></mrow></mrow></math>, <math><mrow id="S2.SS1.p1.3.m3.2.2.1" xref="S2.SS1.p1.3.m3.2.2.1.1.cmml"><mo stretchy="false" id="S2.SS1.p1.3.m3.2.2.1.2" xref="S2.SS1.p1.3.m3.2.2.1.1.cmml">(</mo><mrow id="S2.SS1.p1.3.m3.2.2.1.1" xref="S2.SS1.p1.3.m3.2.2.1.1.cmml"><msub id="S2.SS1.p1.3.m3.2.2.1.1.2" xref="S2.SS1.p1.3.m3.2.2.1.1.2.cmml"><mi id="S2.SS1.p1.3.m3.2.2.1.1.2.2" xref="S2.SS1.p1.3.m3.2.2.1.1.2.2.cmml">P</mi><mn id="S2.SS1.p1.3.m3.2.2.1.1.2.3" xref="S2.SS1.p1.3.m3.2.2.1.1.2.3.cmml">1</mn></msub><mo id="S2.SS1.p1.3.m3.2.2.1.1.1" xref="S2.SS1.p1.3.m3.2.2.1.1.1.cmml">⁢</mo><mrow id="S2.SS1.p1.3.m3.2.2.1.1.3.2" xref="S2.SS1.p1.3.m3.2.2.1.1.cmml"><mo stretchy="false" id="S2.SS1.p1.3.m3.2.2.1.1.3.2.1" xref="S2.SS1.p1.3.m3.2.2.1.1.cmml">(</mo><mi id="S2.SS1.p1.3.m3.1.1" xref="S2.SS1.p1.3.m3.1.1.cmml">I</mi><mo stretchy="false" id="S2.SS1.p1.3.m3.2.2.1.1.3.2.2" xref="S2.SS1.p1.3.m3.2.2.1.1.cmml">)</mo></mrow></mrow><mo stretchy="false" id="S2.SS1.p1.3.m3.2.2.1.3" xref="S2.SS1.p1.3.m3.2.2.1.1.cmml">)</mo></mrow></math>, <math><mrow id="S2.Ex1.m1.5.5" xref="S2.Ex1.m1.5.5.cmml"><mrow id="S2.Ex1.m1.5.5.1.1" xref="S2.Ex1.m1.5.5.1.1.1.cmml"><mo stretchy="false" id="S2.Ex1.m1.5.5.1.1.2" xref="S2.Ex1.m1.5.5.1.1.1.cmml">(</mo><mrow id="S2.Ex1.m1.5.5.1.1.1" xref="S2.Ex1.m1.5.5.1.1.1.cmml"><msub id="S2.Ex1.m1.5.5.1.1.1.2" xref="S2.Ex1.m1.5.5.1.1.1.2.cmml"><mi id="S2.Ex1.m1.5.5.1.1.1.2.2" xref="S2.Ex1.m1.5.5.1.1.1.2.2.cmml">P</mi><mn id="S2.Ex1.m1.5.5.1.1.1.2.3" xref="S2.Ex1.m1.5.5.1.1.1.2.3.cmml">1</mn></msub><mo id="S2.Ex1.m1.5.5.1.1.1.1" xref="S2.Ex1.m1.5.5.1.1.1.1.cmml">⁢</mo><mrow id="S2.Ex1.m1.5.5.1.1.1.3.2" xref="S2.Ex1.m1.5.5.1.1.1.cmml"><mo stretchy="false" id="S2.Ex1.m1.5.5.1.1.1.3.2.1" xref="S2.Ex1.m1.5.5.1.1.1.cmml">(</mo><mi id="S2.Ex1.m1.4.4" xref="S2.Ex1.m1.4.4.cmml">I</mi><mo stretchy="false" id="S2.Ex1.m1.5.5.1.1.1.3.2.2" xref="S2.Ex1.m1.5.5.1.1.1.cmml">)</mo></mrow></mrow><mo stretchy="false" id="S2.Ex1.m1.5.5.1.1.3" xref="S2.Ex1.m1.5.5.1.1.1.cmml">)</mo></mrow><mo id="S2.Ex1.m1.5.5.2" xref="S2.Ex1.m1.5.5.2.cmml">⁢</mo><mrow id="S2.Ex1.m1.3.3" xref="S2.Ex1.m1.5.5.3.1.cmml"><mo id="S2.Ex1.m1.3.3.4" xref="S2.Ex1.m1.5.5.3.1.1.cmml">{</mo><mtable columnspacing="5pt" displaystyle="true" rowspacing="0pt" id="S2.Ex1.m1.3.3.3" xref="S2.Ex1.m1.5.5.3.1.cmml"><mtr id="S2.Ex1.m1.3.3.3a" xref="S2.Ex1.m1.5.5.3.1.cmml"><mtd columnalign="left" id="S2.Ex1.m1.3.3.3b" xref="S2.Ex1.m1.5.5.3.1.cmml"><mrow id="S2.Ex1.m1.1.1.1.1.1.1.1" xref="S2.Ex1.m1.1.1.1.1.1.1.1.1.cmml"><mrow id="S2.Ex1.m1.1.1.1.1.1.1.1.1" xref="S2.Ex1.m1.1.1.1.1.1.1.1.1.cmml"><mtext id="S2.Ex1.m1.1.1.1.1.1.1.1.1.2" xref="S2.Ex1.m1.1.1.1.1.1.1.1.1.2a.cmml">Minimize </mtext><mo id="S2.Ex1.m1.1.1.1.1.1.1.1.1.1" xref="S2.Ex1.m1.1.1.1.1.1.1.1.1.1.cmml">⁢</mo><mrow id="S2.Ex1.m1.1.1.1.1.1.1.1.1.3" xref="S2.Ex1.m1.1.1.1.1.1.1.1.1.3.cmml"><mstyle displaystyle="false" id="S2.Ex1.m1.1.1.1.1.1.1.1.1.3.1" xref="S2.Ex1.m1.1.1.1.1.1.1.1.1.3.1.cmml"><msub id="S2.Ex1.m1.1.1.1.1.1.1.1.1.3.1a" xref="S2.Ex1.m1.1.1.1.1.1.1.1.1.3.1.cmml"><mo largeop="true" symmetric="true" id="S2.Ex1.m1.1.1.1.1.1.1.1.1.3.1.2" xref="S2.Ex1.m1.1.1.1.1.1.1.1.1.3.1.2.cmml">∑</mo><mrow id="S2.Ex1.m1.1.1.1.1.1.1.1.1.3.1.3" xref="S2.Ex1.m1.1.1.1.1.1.1.1.1.3.1.3.cmml"><mi id="S2.Ex1.m1.1.1.1.1.1.1.1.1.3.1.3.2" xref="S2.Ex1.m1.1.1.1.1.1.1.1.1.3.1.3.2.cmml">t</mi><mo id="S2.Ex1.m1.1.1.1.1.1.1.1.1.3.1.3.1" xref="S2.Ex1.m1.1.1.1.1.1.1.1.1.3.1.3.1.cmml">∈</mo><msub id="S2.Ex1.m1.1.1.1.1.1.1.1.1.3.1.3.3" xref="S2.Ex1.m1.1.1.1.1.1.1.1.1.3.1.3.3.cmml"><mi mathvariant="normal" id="S2.Ex1.m1.1.1.1.1.1.1.1.1.3.1.3.3.2" xref="S2.Ex1.m1.1.1.1.1.1.1.1.1.3.1.3.3.2.cmml">Ω</mi><mi id="S2.Ex1.m1.1.1.1.1.1.1.1.1.3.1.3.3.3" xref="S2.Ex1.m1.1.1.1.1.1.1.1.1.3.1.3.3.3.cmml">t</mi></msub></mrow></msub></mstyle><mrow id="S2.Ex1.m1.1.1.1.1.1.1.1.1.3.2" xref="S2.Ex1.m1.1.1.1.1.1.1.1.1.3.2.cmml"><msub id="S2.Ex1.m1.1.1.1.1.1.1.1.1.3.2.2" xref="S2.Ex1.m1.1.1.1.1.1.1.1.1.3.2.2.cmml"><mi id="S2.Ex1.m1.1.1.1.1.1.1.1.1.3.2.2.2" xref="S2.Ex1.m1.1.1.1.1.1.1.1.1.3.2.2.2.cmml">x</mi><mi id="S2.Ex1.m1.1.1.1.1.1.1.1.1.3.2.2.3" xref="S2.Ex1.m1.1.1.1.1.1.1.1.1.3.2.2.3.cmml">t</mi></msub><mo id="S2.Ex1.m1.1.1.1.1.1.1.1.1.3.2.1" xref="S2.Ex1.m1.1.1.1.1.1.1.1.1.3.2.1.cmml">⁢</mo><mtext id="S2.Ex1.m1.1.1.1.1.1.1.1.1.3.2.3" xref="S2.Ex1.m1.1.1.1.1.1.1.1.1.3.2.3a.cmml"> subject to</mtext></mrow></mrow></mrow><mo id="S2.Ex1.m1.1.1.1.1.1.1.1.2" xref="S2.Ex1.m1.1.1.1.1.1.1.1.1.cmml">,</mo></mrow></mtd><mtd id="S2.Ex1.m1.3.3.3c" xref="S2.Ex1.m1.5.5.3.1.1.cmml"/></mtr><mtr id="S2.Ex1.m1.3.3.3d" xref="S2.Ex1.m1.5.5.3.1.cmml"><mtd columnalign="left" id="S2.Ex1.m1.3.3.3e" xref="S2.Ex1.m1.5.5.3.1.cmml"><mrow id="S2.Ex1.m1.2.2.2.2.1.1.9" xref="S2.Ex1.m1.2.2.2.2.1.1.9.1.cmml"><mrow id="S2.Ex1.m1.2.2.2.2.1.1.9.1" xref="S2.Ex1.m1.2.2.2.2.1.1.9.1.cmml"><mrow id="S2.Ex1.m1.2.2.2.2.1.1.9.1.4" xref="S2.Ex1.m1.2.2.2.2.1.1.9.1.4.cmml"><mstyle displaystyle="false" id="S2.Ex1.m1.2.2.2.2.1.1.9.1.4.1" xref="S2.Ex1.m1.2.2.2.2.1.1.9.1.4.1.cmml"><msub id="S2.Ex1.m1.2.2.2.2.1.1.9.1.4.1a" xref="S2.Ex1.m1.2.2.2.2.1.1.9.1.4.1.cmml"><mo largeop="true" symmetric="true" id="S2.Ex1.m1.2.2.2.2.1.1.9.1.4.1.2" xref="S2.Ex1.m1.2.2.2.2.1.1.9.1.4.1.2.cmml">∑</mo><mrow id="S2.Ex1.m1.2.2.2.2.1.1.4.4.4" xref="S2.Ex1.m1.2.2.2.2.1.1.4.4.5.cmml"><mrow id="S2.Ex1.m1.2.2.2.2.1.1.3.3.3.1" xref="S2.Ex1.m1.2.2.2.2.1.1.3.3.3.1.cmml"><mrow id="S2.Ex1.m1.2.2.2.2.1.1.3.3.3.1.2" xref="S2.Ex1.m1.2.2.2.2.1.1.3.3.3.1.2.cmml"><mrow id="S2.Ex1.m1.2.2.2.2.1.1.3.3.3.1.2.2" xref="S2.Ex1.m1.2.2.2.2.1.1.3.3.3.1.2.2.cmml"><mi id="S2.Ex1.m1.2.2.2.2.1.1.3.3.3.1.2.2.2" xref="S2.Ex1.m1.2.2.2.2.1.1.3.3.3.1.2.2.2.cmml">t</mi><mo id="S2.Ex1.m1.2.2.2.2.1.1.3.3.3.1.2.2.1" xref="S2.Ex1.m1.2.2.2.2.1.1.3.3.3.1.2.2.1.cmml">/</mo><mi id="S2.Ex1.m1.2.2.2.2.1.1.3.3.3.1.2.2.3" xref="S2.Ex1.m1.2.2.2.2.1.1.3.3.3.1.2.2.3.cmml">C</mi></mrow><mo id="S2.Ex1.m1.2.2.2.2.1.1.3.3.3.1.2.1" xref="S2.Ex1.m1.2.2.2.2.1.1.3.3.3.1.2.1.cmml">⁢</mo><mrow id="S2.Ex1.m1.2.2.2.2.1.1.3.3.3.1.2.3.2" xref="S2.Ex1.m1.2.2.2.2.1.1.3.3.3.1.2.3.1.cmml"><mo stretchy="false" id="S2.Ex1.m1.2.2.2.2.1.1.3.3.3.1.2.3.2.1" xref="S2.Ex1.m1.2.2.2.2.1.1.3.3.3.1.2.3.1.cmml">(</mo><mi id="S2.Ex1.m1.2.2.2.2.1.1.1.1.1" xref="S2.Ex1.m1.2.2.2.2.1.1.1.1.1.cmml">t</mi><mo id="S2.Ex1.m1.2.2.2.2.1.1.3.3.3.1.2.3.2.2" xref="S2.Ex1.m1.2.2.2.2.1.1.3.3.3.1.2.3.1.cmml">,</mo><mi id="S2.Ex1.m1.2.2.2.2.1.1.2.2.2" xref="S2.Ex1.m1.2.2.2.2.1.1.2.2.2.cmml">i</mi><mo stretchy="false" id="S2.Ex1.m1.2.2.2.2.1.1.3.3.3.1.2.3.2.3" xref="S2.Ex1.m1.2.2.2.2.1.1.3.3.3.1.2.3.1.cmml">)</mo></mrow></mrow><mo id="S2.Ex1.m1.2.2.2.2.1.1.3.3.3.1.1" xref="S2.Ex1.m1.2.2.2.2.1.1.3.3.3.1.1.cmml">≥</mo><mi id="S2.Ex1.m1.2.2.2.2.1.1.3.3.3.1.3" xref="S2.Ex1.m1.2.2.2.2.1.1.3.3.3.1.3.cmml">n</mi></mrow><mo id="S2.Ex1.m1.2.2.2.2.1.1.4.4.4.3" xref="S2.Ex1.m1.2.2.2.2.1.1.4.4.5a.cmml">,</mo><mrow id="S2.Ex1.m1.2.2.2.2.1.1.4.4.4.2" xref="S2.Ex1.m1.2.2.2.2.1.1.4.4.4.2.cmml"><mi id="S2.Ex1.m1.2.2.2.2.1.1.4.4.4.2.2" xref="S2.Ex1.m1.2.2.2.2.1.1.4.4.4.2.2.cmml">t</mi><mo id="S2.Ex1.m1.2.2.2.2.1.1.4.4.4.2.1" xref="S2.Ex1.m1.2.2.2.2.1.1.4.4.4.2.1.cmml">∈</mo><msub id="S2.Ex1.m1.2.2.2.2.1.1.4.4.4.2.3" xref="S2.Ex1.m1.2.2.2.2.1.1.4.4.4.2.3.cmml"><mi mathvariant="normal" id="S2.Ex1.m1.2.2.2.2.1.1.4.4.4.2.3.2" xref="S2.Ex1.m1.2.2.2.2.1.1.4.4.4.2.3.2.cmml">Ω</mi><mi id="S2.Ex1.m1.2.2.2.2.1.1.4.4.4.2.3.3" xref="S2.Ex1.m1.2.2.2.2.1.1.4.4.4.2.3.3.cmml">t</mi></msub></mrow></mrow></msub></mstyle><msub id="S2.Ex1.m1.2.2.2.2.1.1.9.1.4.2" xref="S2.Ex1.m1.2.2.2.2.1.1.9.1.4.2.cmml"><mi id="S2.Ex1.m1.2.2.2.2.1.1.9.1.4.2.2" xref="S2.Ex1.m1.2.2.2.2.1.1.9.1.4.2.2.cmml">x</mi><mi id="S2.Ex1.m1.2.2.2.2.1.1.9.1.4.2.3" xref="S2.Ex1.m1.2.2.2.2.1.1.9.1.4.2.3.cmml">t</mi></msub></mrow><mo id="S2.Ex1.m1.2.2.2.2.1.1.9.1.3" xref="S2.Ex1.m1.2.2.2.2.1.1.9.1.3.cmml">≥</mo><mrow id="S2.Ex1.m1.2.2.2.2.1.1.9.1.2.2" xref="S2.Ex1.m1.2.2.2.2.1.1.9.1.2.3.cmml"><mrow id="S2.Ex1.m1.2.2.2.2.1.1.9.1.1.1.1" xref="S2.Ex1.m1.2.2.2.2.1.1.9.1.1.1.1.cmml"><mi id="S2.Ex1.m1.2.2.2.2.1.1.9.1.1.1.1.2" xref="S2.Ex1.m1.2.2.2.2.1.1.9.1.1.1.1.2.cmml">R</mi><mo id="S2.Ex1.m1.2.2.2.2.1.1.9.1.1.1.1.1" xref="S2.Ex1.m1.2.2.2.2.1.1.9.1.1.1.1.1.cmml">⁢</mo><mrow id="S2.Ex1.m1.2.2.2.2.1.1.9.1.1.1.1.3.2" xref="S2.Ex1.m1.2.2.2.2.1.1.9.1.1.1.1.3.1.cmml"><mo stretchy="false" id="S2.Ex1.m1.2.2.2.2.1.1.9.1.1.1.1.3.2.1" xref="S2.Ex1.m1.2.2.2.2.1.1.9.1.1.1.1.3.1.cmml">(</mo><mi id="S2.Ex1.m1.2.2.2.2.1.1.5" xref="S2.Ex1.m1.2.2.2.2.1.1.5.cmml">I</mi><mo id="S2.Ex1.m1.2.2.2.2.1.1.9.1.1.1.1.3.2.2" xref="S2.Ex1.m1.2.2.2.2.1.1.9.1.1.1.1.3.1.cmml">,</mo><mi id="S2.Ex1.m1.2.2.2.2.1.1.6" xref="S2.Ex1.m1.2.2.2.2.1.1.6.cmml">i</mi><mo id="S2.Ex1.m1.2.2.2.2.1.1.9.1.1.1.1.3.2.3" xref="S2.Ex1.m1.2.2.2.2.1.1.9.1.1.1.1.3.1.cmml">,</mo><mi id="S2.Ex1.m1.2.2.2.2.1.1.7" xref="S2.Ex1.m1.2.2.2.2.1.1.7.cmml">n</mi><mo stretchy="false" id="S2.Ex1.m1.2.2.2.2.1.1.9.1.1.1.1.3.2.4" xref="S2.Ex1.m1.2.2.2.2.1.1.9.1.1.1.1.3.1.cmml">)</mo></mrow></mrow><mo separator="true" id="S2.Ex1.m1.2.2.2.2.1.1.9.1.2.2.3" xref="S2.Ex1.m1.2.2.2.2.1.1.9.1.2.3.cmml">  </mo><mrow id="S2.Ex1.m1.2.2.2.2.1.1.9.1.2.2.2" xref="S2.Ex1.m1.2.2.2.2.1.1.9.1.2.2.2.cmml"><mo id="S2.Ex1.m1.2.2.2.2.1.1.9.1.2.2.2.1" xref="S2.Ex1.m1.2.2.2.2.1.1.9.1.2.2.2.1.cmml">∀</mo><mi id="S2.Ex1.m1.2.2.2.2.1.1.9.1.2.2.2.2" xref="S2.Ex1.m1.2.2.2.2.1.1.9.1.2.2.2.2.cmml">i</mi></mrow><mo id="S2.Ex1.m1.2.2.2.2.1.1.9.1.2.2.4" xref="S2.Ex1.m1.2.2.2.2.1.1.9.1.2.3.cmml">,</mo><mi id="S2.Ex1.m1.2.2.2.2.1.1.8" xref="S2.Ex1.m1.2.2.2.2.1.1.8.cmml">n</mi></mrow></mrow><mo id="S2.Ex1.m1.2.2.2.2.1.1.9.2" xref="S2.Ex1.m1.2.2.2.2.1.1.9.1.cmml">,</mo></mrow></mtd><mtd id="S2.Ex1.m1.3.3.3f" xref="S2.Ex1.m1.5.5.3.1.1.cmml"/></mtr><mtr id="S2.Ex1.m1.3.3.3g" xref="S2.Ex1.m1.5.5.3.1.cmml"><mtd columnalign="left" id="S2.Ex1.m1.3.3.3h" xref="S2.Ex1.m1.5.5.3.1.cmml"><mrow id="S2.Ex1.m1.3.3.3.3.1.1.4" xref="S2.Ex1.m1.3.3.3.3.1.1.5.cmml"><mrow id="S2.Ex1.m1.3.3.3.3.1.1.3.1" xref="S2.Ex1.m1.3.3.3.3.1.1.3.1.cmml"><msub id="S2.Ex1.m1.3.3.3.3.1.1.3.1.2" xref="S2.Ex1.m1.3.3.3.3.1.1.3.1.2.cmml"><mi id="S2.Ex1.m1.3.3.3.3.1.1.3.1.2.2" xref="S2.Ex1.m1.3.3.3.3.1.1.3.1.2.2.cmml">x</mi><mi id="S2.Ex1.m1.3.3.3.3.1.1.3.1.2.3" xref="S2.Ex1.m1.3.3.3.3.1.1.3.1.2.3.cmml">t</mi></msub><mo id="S2.Ex1.m1.3.3.3.3.1.1.3.1.1" xref="S2.Ex1.m1.3.3.3.3.1.1.3.1.1.cmml">∈</mo><mrow id="S2.Ex1.m1.3.3.3.3.1.1.3.1.3.2" xref="S2.Ex1.m1.3.3.3.3.1.1.3.1.3.1.cmml"><mo stretchy="false" id="S2.Ex1.m1.3.3.3.3.1.1.3.1.3.2.1" xref="S2.Ex1.m1.3.3.3.3.1.1.3.1.3.1.cmml">{</mo><mn id="S2.Ex1.m1.3.3.3.3.1.1.1" xref="S2.Ex1.m1.3.3.3.3.1.1.1.cmml">0</mn><mo id="S2.Ex1.m1.3.3.3.3.1.1.3.1.3.2.2" xref="S2.Ex1.m1.3.3.3.3.1.1.3.1.3.1.cmml">,</mo><mn id="S2.Ex1.m1.3.3.3.3.1.1.2" xref="S2.Ex1.m1.3.3.3.3.1.1.2.cmml">1</mn><mo stretchy="false" id="S2.Ex1.m1.3.3.3.3.1.1.3.1.3.2.3" xref="S2.Ex1.m1.3.3.3.3.1.1.3.1.3.1.cmml">}</mo></mrow></mrow><mo mathsize="70%" mathvariant="italic" separator="true" stretchy="false" id="S2.Ex1.m1.3.3.3.3.1.1.4.3" xref="S2.Ex1.m1.3.3.3.3.1.1.5a.cmml">  </mo><mrow id="S2.Ex1.m1.3.3.3.3.1.1.4.2" xref="S2.Ex1.m1.3.3.3.3.1.1.4.2.cmml"><mi id="S2.Ex1.m1.3.3.3.3.1.1.4.2.2" xref="S2.Ex1.m1.3.3.3.3.1.1.4.2.2.cmml">t</mi><mo id="S2.Ex1.m1.3.3.3.3.1.1.4.2.1" xref="S2.Ex1.m1.3.3.3.3.1.1.4.2.1.cmml">∈</mo><msub id="S2.Ex1.m1.3.3.3.3.1.1.4.2.3" xref="S2.Ex1.m1.3.3.3.3.1.1.4.2.3.cmml"><mi mathvariant="normal" id="S2.Ex1.m1.3.3.3.3.1.1.4.2.3.2" xref="S2.Ex1.m1.3.3.3.3.1.1.4.2.3.2.cmml">Ω</mi><mi id="S2.Ex1.m1.3.3.3.3.1.1.4.2.3.3" xref="S2.Ex1.m1.3.3.3.3.1.1.4.2.3.3.cmml">t</mi></msub></mrow></mrow></mtd><mtd id="S2.Ex1.m1.3.3.3i" xref="S2.Ex1.m1.5.5.3.1.1.cmml"/></mtr></mtable></mrow></mrow></math>, <math><mrow id="S2.SS1.p1.4.m1.2.3" xref="S2.SS1.p1.4.m1.2.3.cmml"><msub id="S2.SS1.p1.4.m1.2.3.2" xref="S2.SS1.p1.4.m1.2.3.2.cmml"><mi id="S2.SS1.p1.4.m1.2.3.2.2" xref="S2.SS1.p1.4.m1.2.3.2.2.cmml">w</mi><mi id="S2.SS1.p1.4.m1.2.3.2.3" xref="S2.SS1.p1.4.m1.2.3.2.3.cmml">I</mi></msub><mo id="S2.SS1.p1.4.m1.2.3.1" xref="S2.SS1.p1.4.m1.2.3.1.cmml">=</mo><mrow id="S2.SS1.p1.4.m1.2.3.3" xref="S2.SS1.p1.4.m1.2.3.3.cmml"><mrow id="S2.SS1.p1.4.m1.2.3.3.2" xref="S2.SS1.p1.4.m1.2.3.3.2.cmml"><mrow id="S2.SS1.p1.4.m1.2.3.3.2.2" xref="S2.SS1.p1.4.m1.2.3.3.2.2.cmml"><mi id="S2.SS1.p1.4.m1.2.3.3.2.2.2" xref="S2.SS1.p1.4.m1.2.3.3.2.2.2.cmml">m</mi><mo id="S2.SS1.p1.4.m1.2.3.3.2.2.1" xref="S2.SS1.p1.4.m1.2.3.3.2.2.1.cmml">⁢</mo><mi id="S2.SS1.p1.4.m1.2.3.3.2.2.3" xref="S2.SS1.p1.4.m1.2.3.3.2.2.3.cmml">i</mi><mo id="S2.SS1.p1.4.m1.2.3.3.2.2.1a" xref="S2.SS1.p1.4.m1.2.3.3.2.2.1.cmml">⁢</mo><mi id="S2.SS1.p1.4.m1.2.3.3.2.2.4" xref="S2.SS1.p1.4.m1.2.3.3.2.2.4.cmml">n</mi><mo id="S2.SS1.p1.4.m1.2.3.3.2.2.1b" xref="S2.SS1.p1.4.m1.2.3.3.2.2.1.cmml">⁢</mo><mi id="S2.SS1.p1.4.m1.2.3.3.2.2.5" xref="S2.SS1.p1.4.m1.2.3.3.2.2.5.cmml">t</mi><mo id="S2.SS1.p1.4.m1.2.3.3.2.2.1c" xref="S2.SS1.p1.4.m1.2.3.3.2.2.1.cmml">⁢</mo><mi id="S2.SS1.p1.4.m1.2.3.3.2.2.6" xref="S2.SS1.p1.4.m1.2.3.3.2.2.6.cmml">e</mi><mo id="S2.SS1.p1.4.m1.2.3.3.2.2.1d" xref="S2.SS1.p1.4.m1.2.3.3.2.2.1.cmml">⁢</mo><mi id="S2.SS1.p1.4.m1.2.3.3.2.2.7" xref="S2.SS1.p1.4.m1.2.3.3.2.2.7.cmml">c</mi><mo id="S2.SS1.p1.4.m1.2.3.3.2.2.1e" xref="S2.SS1.p1.4.m1.2.3.3.2.2.1.cmml">⁢</mo><mrow id="S2.SS1.p1.4.m1.2.3.3.2.2.8.2" xref="S2.SS1.p1.4.m1.2.3.3.2.2.cmml"><mo stretchy="false" id="S2.SS1.p1.4.m1.2.3.3.2.2.8.2.1" xref="S2.SS1.p1.4.m1.2.3.3.2.2.cmml">(</mo><mi id="S2.SS1.p1.4.m1.1.1" xref="S2.SS1.p1.4.m1.1.1.cmml">I</mi><mo stretchy="false" id="S2.SS1.p1.4.m1.2.3.3.2.2.8.2.2" xref="S2.SS1.p1.4.m1.2.3.3.2.2.cmml">)</mo></mrow></mrow><mo id="S2.SS1.p1.4.m1.2.3.3.2.1" xref="S2.SS1.p1.4.m1.2.3.3.2.1.cmml">×</mo><mi id="S2.SS1.p1.4.m1.2.3.3.2.3" xref="S2.SS1.p1.4.m1.2.3.3.2.3.cmml">T</mi></mrow><mo id="S2.SS1.p1.4.m1.2.3.3.1" xref="S2.SS1.p1.4.m1.2.3.3.1.cmml">⁢</mo><mrow id="S2.SS1.p1.4.m1.2.3.3.3.2" xref="S2.SS1.p1.4.m1.2.3.3.cmml"><mo stretchy="false" id="S2.SS1.p1.4.m1.2.3.3.3.2.1" xref="S2.SS1.p1.4.m1.2.3.3.cmml">(</mo><mi id="S2.SS1.p1.4.m1.2.2" xref="S2.SS1.p1.4.m1.2.2.cmml">I</mi><mo stretchy="false" id="S2.SS1.p1.4.m1.2.3.3.3.2.2" xref="S2.SS1.p1.4.m1.2.3.3.cmml">)</mo></mrow></mrow></mrow></math>

Correct Categorie: cs

Guessed Categorie: astro-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/9701110

Formulas:

1-

ρ (r) = ρ_{o} {(r_{o} / r)}^{2}

2-

ρ (r) = σ_{v}^{2} / 2 G π r^{2}

3-

(θ_{x}, θ_{y})

4-

α_{x} = \frac{2 Σ_{o}}{Σ_{c r}} θ_{x} \frac{1 - γ^{'}}{1 - γ_{o}^{2}}

5-

α_{y} = \frac{2 Σ_{o}}{Σ_{c r}} θ_{y} \frac{1 - γ^{'}}{γ^{'} (1 - γ_{o}^{2})} .

6-

Σ_{c r}^{- 1} = \frac{4 π G D_{l} D_{l s}}{c^{2} D_{s}}

7-

(θ_{x}, θ_{y})

8-

I_{A} / I_{B} = 1.3

9-

a / b = 2.4 \pm 0.2

10-

H_{o} = 100 h {kms}^{- 1} {Mpc}^{- 1}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: astro-ph

Result: correct

Paper: https://arxiv.org/abs/quant-ph/0305092

Formulas:

1-

| ψ ⟩ = ({| H ⟩}_{1} {| H ⟩}_{2} - {| V ⟩}_{1} {| V ⟩}_{2}) / \sqrt{2} .

2-

| ψ ⟩ = ({| H ⟩}_{T} {| V ⟩}_{R} + {| V ⟩}_{T} {| H ⟩}_{R}) / \sqrt{2},

3-

θ_{T} = π / 8

4-

θ_{T} = π / 8

5-

V = [C (0) - C (π / 8)] / [C (0) + C (π / 8)]

6-

C (θ_{T})

7-

C_{T T, R T}

8-

C_{T R, R R}

9-

C_{T T, T R}

10-

C_{T T, T R}

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: hep-th

Result: incorrect

Paper: https://arxiv.org/abs/1603.03769

Formulas:

1-

[\frac{\partial}{v \partial t} + 𝛀 \cdot \nabla + μ_{a} (𝒓) + μ_{s} (𝒓)] I (𝒓, 𝛀, t) = μ_{s} (𝒓) \int_{2 π} 𝑑 𝛀^{'} P (𝒓, 𝛀 \cdot 𝛀^{'}) I (𝒓, 𝛀^{'}, t) + q (𝒓, 𝛀, t),

2-

I (𝒓, 𝛀, t)

3-

𝒓 = (x, y)

4-

𝛀 = (Ω_{x}, Ω_{y}) = (\cos θ, \sin θ)

5-

μ_{a} (𝒓)

6-

μ_{s} (𝒓)

7-

P (𝒓, 𝛀 \cdot 𝛀^{'})

8-

q (𝒓, 𝛀, t) [W / {cm}^{2} rad]

9-

P (𝒓, 𝛀 \cdot 𝛀^{'})

10-

P (𝒓, 𝛀 \cdot 𝛀^{'}) = \frac{1}{2 π} \frac{1 - {g (𝒓)}^{2}}{1 + {g (𝒓)}^{2} - 2 g (𝒓) 𝛀 \cdot 𝛀^{'}},

Formulas (html):

Correct Categorie: physics

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/hep-ph/9812331

Formulas:

1-

{(M^{2} / Q^{2})}^{j}

2-

g_{1}^{\pm} (x)

3-

x \frac{d}{d x} x \frac{d}{d x} [\frac{x}{{(1 + 4 M^{2} x^{2} / Q^{2})}^{1 / 2}} \frac{G_{1}^{\pm} (ξ)}{ξ}],

4-

g_{2}^{\pm} (x)

5-

- x \frac{d^{2}}{d x^{2}} x [\frac{x}{{(1 + 4 M^{2} x^{2} / Q^{2})}^{1 / 2}} \frac{G_{1}^{\pm} (ξ)}{ξ}],

6-

g_{3}^{\pm} (x)

7-

2 x^{2} \frac{d^{2}}{d x^{2}} [\frac{x^{2}}{{(1 + 4 M^{2} x^{2} / Q^{2})}^{1 / 2}} \frac{G_{2}^{\pm} (ξ)}{ξ^{2}}],

8-

g_{4}^{\pm} (x)

9-

- x^{2} \frac{d}{d x} x \frac{d^{2}}{d x^{2}} [\frac{x^{2}}{{(1 + 4 M^{2} x^{2} / Q^{2})}^{1 / 2}} \frac{G_{2}^{\pm} (ξ)}{ξ^{2}}],

10-

g_{5}^{\pm} (x)

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: cond-mat

Result: incorrect

Paper: https://arxiv.org/abs/0901.1019

Formulas:

1-

10^{- 7} - 10^{- 6}

2-

J_{K_{a} K_{c}}

3-

J_{K_{- 1} K_{+ 1}}

4-

1.8 - 27 \times 10^{13}

5-

0.095 - 2.4 \times 10^{13}

6-

10^{- 4} - 10^{- 3}

7-

(1 - 5) \times 10^{- 4}

8-

Y_{pd} \times I_{UV} \times σ_{gr} \times f_{x} = 4.57 \times 10^{4} \times {(\frac{T}{m_{x}})}^{\frac{1}{2}} \times σ_{gr} \times n_{x}^{g}

9-

f_{x} = \frac{n_{x}^{i}}{n^{i}}

10-

(1 - 3) \times 10^{- 3}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: gr-qc

Result: incorrect

Run 12593918 (TestAgent)