Run 11332251

Paper: https://arxiv.org/abs/hep-th/0303234

Formulas:

1-

b_{3} (X)

2-

b_{3} (X)

3-

b_{3} (X)

4-

𝒪 (10^{2})

5-

{(T e V)}^{4}

6-

10 T e V

7-

M_{G U T}

8-

10^{13} G e V

9-

L \sim λ H ψ_{1} ψ_{2}

10-

λ \sim e^{- 2 π V o l (Σ)}

Formulas (html):

Correct Categorie: hep-th

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0604090

Formulas:

1-

w \equiv γ - 1 = p / ρ

2-

i = 1, \dots, N

3-

V_{i} (ϕ_{i})

4-

S_{t o t} = S_{g} + S_{d e}

5-

S_{g} = \int d^{4} x \sqrt{- g} \frac{R}{6},

6-

S_{d e} = - \int d^{4} x \sqrt{- g} \sum_{i = 1}^{N} V_{i} (ϕ_{i}) F_{i} (X_{i}) .

7-

X_{i} \equiv g^{μ ν} ϕ_{i μ} ϕ_{i ν},

8-

ϕ_{i μ} = \partial_{μ} ϕ_{i}

9-

T_{μ ν} = \sum_{i = 1}^{N} V_{i} [F_{i}^{'} ϕ_{i μ} ϕ_{i ν} - g_{μ ν} F_{i}] .

10-

ρ_{i} = V_{i} [F_{i} - 2 X_{i} F_{i}^{'}], p_{i} = - V_{i} F_{i} .

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1805.01895

Formulas:

1-

- \frac{ℏ^{2}}{2 m} \frac{d^{2} ϕ}{d x^{2}} - V (x) ϕ = E ϕ,

2-

V (x) > 0

3-

V (x) = {\begin{matrix} V (x) & if | x | < δ x / 2 \\ 0 & otherwise, \end{matrix}

4-

V (x) = V (0)

5-

ϕ (x) = ϕ (0)

6-

- \frac{ℏ^{2}}{2 m} \frac{d^{2} ϕ}{d x^{2}} = E ϕ

7-

V (x) = V_{0}

8-

- \frac{ℏ^{2}}{2 m} \frac{d^{2} ϕ (0)}{d x^{2}} - V_{0} ϕ (0) = E ϕ (0) .

9-

- \frac{ℏ^{2}}{2 m} \frac{d^{2} ϕ}{d x^{2}} = E ϕ .

10-

ϕ = {\begin{matrix} A e^{κ x} x < - δ x / 2 \\ ϕ (0) x \in (- δ x / 2, δ x / 2) \\ B e^{- κ x} x > δ x / 2, where κ^{2} = - 2 m E / ℏ^{2} . \end{matrix}

Formulas (html):

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id="S2.E2.m1.1.1.1.1.1.1.1.m1.1.2.3.1" xref="S2.E2.m1.1.1.1.1.1.1.1.m1.1.2.3.1.cmml">/</mo><mn id="S2.E2.m1.1.1.1.1.1.1.1.m1.1.2.3.3" xref="S2.E2.m1.1.1.1.1.1.1.1.m1.1.2.3.3.cmml">2</mn></mrow></mrow></mrow></mtd></mtr><mtr id="S2.E2.m1.3.3d" xref="S2.E2.m1.3.3.cmml"><mtd columnalign="left" id="S2.E2.m1.3.3e" xref="S2.E2.m1.3.3.cmml"><mn id="S2.E2.m1.3.3.3.2.1" xref="S2.E2.m1.3.3.3.2.1.cmml">0</mn></mtd><mtd columnalign="left" id="S2.E2.m1.3.3f" xref="S2.E2.m1.3.3.cmml"><mrow id="S2.E2.m1.3.3.3.1.1.3" xref="S2.E2.m1.3.3.3.1.1.1a.cmml"><mtext id="S2.E2.m1.3.3.3.1.1.1" xref="S2.E2.m1.3.3.3.1.1.1.cmml">otherwise</mtext><mo id="S2.E2.m1.3.3.3.1.1.3.1" xref="S2.E2.m1.3.3.3.1.1.1a.cmml">,</mo></mrow></mtd></mtr></mtable><mi id="S2.E2.m1.4.5.3.2.2" xref="S2.E2.m1.4.5.3.1.1.cmml"/></mrow></mrow></math>, <math><mrow id="S2.p2.1.m1.2.3" xref="S2.p2.1.m1.2.3.cmml"><mrow id="S2.p2.1.m1.2.3.2" xref="S2.p2.1.m1.2.3.2.cmml"><mi id="S2.p2.1.m1.2.3.2.2" xref="S2.p2.1.m1.2.3.2.2.cmml">V</mi><mo id="S2.p2.1.m1.2.3.2.1" xref="S2.p2.1.m1.2.3.2.1.cmml">⁢</mo><mrow id="S2.p2.1.m1.2.3.2.3.2" xref="S2.p2.1.m1.2.3.2.cmml"><mo stretchy="false" id="S2.p2.1.m1.2.3.2.3.2.1" xref="S2.p2.1.m1.2.3.2.cmml">(</mo><mi id="S2.p2.1.m1.1.1" xref="S2.p2.1.m1.1.1.cmml">x</mi><mo stretchy="false" id="S2.p2.1.m1.2.3.2.3.2.2" xref="S2.p2.1.m1.2.3.2.cmml">)</mo></mrow></mrow><mo id="S2.p2.1.m1.2.3.1" xref="S2.p2.1.m1.2.3.1.cmml">=</mo><mrow id="S2.p2.1.m1.2.3.3" xref="S2.p2.1.m1.2.3.3.cmml"><mi id="S2.p2.1.m1.2.3.3.2" xref="S2.p2.1.m1.2.3.3.2.cmml">V</mi><mo id="S2.p2.1.m1.2.3.3.1" xref="S2.p2.1.m1.2.3.3.1.cmml">⁢</mo><mrow id="S2.p2.1.m1.2.3.3.3.2" xref="S2.p2.1.m1.2.3.3.cmml"><mo stretchy="false" id="S2.p2.1.m1.2.3.3.3.2.1" xref="S2.p2.1.m1.2.3.3.cmml">(</mo><mn id="S2.p2.1.m1.2.2" xref="S2.p2.1.m1.2.2.cmml">0</mn><mo stretchy="false" id="S2.p2.1.m1.2.3.3.3.2.2" xref="S2.p2.1.m1.2.3.3.cmml">)</mo></mrow></mrow></mrow></math>, <math><mrow id="S2.p2.2.m2.2.3" xref="S2.p2.2.m2.2.3.cmml"><mrow id="S2.p2.2.m2.2.3.2" xref="S2.p2.2.m2.2.3.2.cmml"><mi id="S2.p2.2.m2.2.3.2.2" xref="S2.p2.2.m2.2.3.2.2.cmml">ϕ</mi><mo id="S2.p2.2.m2.2.3.2.1" xref="S2.p2.2.m2.2.3.2.1.cmml">⁢</mo><mrow id="S2.p2.2.m2.2.3.2.3.2" xref="S2.p2.2.m2.2.3.2.cmml"><mo stretchy="false" id="S2.p2.2.m2.2.3.2.3.2.1" xref="S2.p2.2.m2.2.3.2.cmml">(</mo><mi id="S2.p2.2.m2.1.1" xref="S2.p2.2.m2.1.1.cmml">x</mi><mo stretchy="false" id="S2.p2.2.m2.2.3.2.3.2.2" xref="S2.p2.2.m2.2.3.2.cmml">)</mo></mrow></mrow><mo id="S2.p2.2.m2.2.3.1" xref="S2.p2.2.m2.2.3.1.cmml">=</mo><mrow id="S2.p2.2.m2.2.3.3" xref="S2.p2.2.m2.2.3.3.cmml"><mi id="S2.p2.2.m2.2.3.3.2" xref="S2.p2.2.m2.2.3.3.2.cmml">ϕ</mi><mo id="S2.p2.2.m2.2.3.3.1" xref="S2.p2.2.m2.2.3.3.1.cmml">⁢</mo><mrow id="S2.p2.2.m2.2.3.3.3.2" xref="S2.p2.2.m2.2.3.3.cmml"><mo stretchy="false" id="S2.p2.2.m2.2.3.3.3.2.1" xref="S2.p2.2.m2.2.3.3.cmml">(</mo><mn id="S2.p2.2.m2.2.2" xref="S2.p2.2.m2.2.2.cmml">0</mn><mo stretchy="false" id="S2.p2.2.m2.2.3.3.3.2.2" xref="S2.p2.2.m2.2.3.3.cmml">)</mo></mrow></mrow></mrow></math>, <math><mrow id="S2.Ex1.m1.1.1" xref="S2.Ex1.m1.1.1.cmml"><mrow id="S2.Ex1.m1.1.1.2" xref="S2.Ex1.m1.1.1.2.cmml"><mo id="S2.Ex1.m1.1.1.2.1" xref="S2.Ex1.m1.1.1.2.1.cmml">-</mo><mrow id="S2.Ex1.m1.1.1.2.2" xref="S2.Ex1.m1.1.1.2.2.cmml"><mfrac id="S2.Ex1.m1.1.1.2.2.2" xref="S2.Ex1.m1.1.1.2.2.2.cmml"><msup id="S2.Ex1.m1.1.1.2.2.2.2" xref="S2.Ex1.m1.1.1.2.2.2.2.cmml"><mi mathvariant="normal" id="S2.Ex1.m1.1.1.2.2.2.2.2" xref="S2.Ex1.m1.1.1.2.2.2.2.2.cmml">ℏ</mi><mn id="S2.Ex1.m1.1.1.2.2.2.2.3" xref="S2.Ex1.m1.1.1.2.2.2.2.3.cmml">2</mn></msup><mrow id="S2.Ex1.m1.1.1.2.2.2.3" xref="S2.Ex1.m1.1.1.2.2.2.3.cmml"><mn id="S2.Ex1.m1.1.1.2.2.2.3.2" xref="S2.Ex1.m1.1.1.2.2.2.3.2.cmml">2</mn><mo id="S2.Ex1.m1.1.1.2.2.2.3.1" xref="S2.Ex1.m1.1.1.2.2.2.3.1.cmml">⁢</mo><mi id="S2.Ex1.m1.1.1.2.2.2.3.3" xref="S2.Ex1.m1.1.1.2.2.2.3.3.cmml">m</mi></mrow></mfrac><mo id="S2.Ex1.m1.1.1.2.2.1" xref="S2.Ex1.m1.1.1.2.2.1.cmml">⁢</mo><mfrac id="S2.Ex1.m1.1.1.2.2.3" xref="S2.Ex1.m1.1.1.2.2.3.cmml"><mrow id="S2.Ex1.m1.1.1.2.2.3.2" xref="S2.Ex1.m1.1.1.2.2.3.2.cmml"><msup id="S2.Ex1.m1.1.1.2.2.3.2.2" xref="S2.Ex1.m1.1.1.2.2.3.2.2.cmml"><mi id="S2.Ex1.m1.1.1.2.2.3.2.2.2" xref="S2.Ex1.m1.1.1.2.2.3.2.2.2.cmml">d</mi><mn id="S2.Ex1.m1.1.1.2.2.3.2.2.3" xref="S2.Ex1.m1.1.1.2.2.3.2.2.3.cmml">2</mn></msup><mo id="S2.Ex1.m1.1.1.2.2.3.2.1" xref="S2.Ex1.m1.1.1.2.2.3.2.1.cmml">⁢</mo><mi id="S2.Ex1.m1.1.1.2.2.3.2.3" xref="S2.Ex1.m1.1.1.2.2.3.2.3.cmml">ϕ</mi></mrow><mrow id="S2.Ex1.m1.1.1.2.2.3.3" xref="S2.Ex1.m1.1.1.2.2.3.3.cmml"><mi id="S2.Ex1.m1.1.1.2.2.3.3.2" xref="S2.Ex1.m1.1.1.2.2.3.3.2.cmml">d</mi><mo id="S2.Ex1.m1.1.1.2.2.3.3.1" xref="S2.Ex1.m1.1.1.2.2.3.3.1.cmml">⁢</mo><msup id="S2.Ex1.m1.1.1.2.2.3.3.3" xref="S2.Ex1.m1.1.1.2.2.3.3.3.cmml"><mi id="S2.Ex1.m1.1.1.2.2.3.3.3.2" xref="S2.Ex1.m1.1.1.2.2.3.3.3.2.cmml">x</mi><mn id="S2.Ex1.m1.1.1.2.2.3.3.3.3" xref="S2.Ex1.m1.1.1.2.2.3.3.3.3.cmml">2</mn></msup></mrow></mfrac></mrow></mrow><mo id="S2.Ex1.m1.1.1.1" xref="S2.Ex1.m1.1.1.1.cmml">=</mo><mrow id="S2.Ex1.m1.1.1.3" xref="S2.Ex1.m1.1.1.3.cmml"><mi id="S2.Ex1.m1.1.1.3.2" xref="S2.Ex1.m1.1.1.3.2.cmml">E</mi><mo id="S2.Ex1.m1.1.1.3.1" xref="S2.Ex1.m1.1.1.3.1.cmml">⁢</mo><mi id="S2.Ex1.m1.1.1.3.3" xref="S2.Ex1.m1.1.1.3.3.cmml">ϕ</mi></mrow></mrow></math>, <math><mrow id="S2.p2.3.m1.1.2" xref="S2.p2.3.m1.1.2.cmml"><mrow id="S2.p2.3.m1.1.2.2" xref="S2.p2.3.m1.1.2.2.cmml"><mi id="S2.p2.3.m1.1.2.2.2" xref="S2.p2.3.m1.1.2.2.2.cmml">V</mi><mo id="S2.p2.3.m1.1.2.2.1" xref="S2.p2.3.m1.1.2.2.1.cmml">⁢</mo><mrow id="S2.p2.3.m1.1.2.2.3.2" xref="S2.p2.3.m1.1.2.2.cmml"><mo stretchy="false" id="S2.p2.3.m1.1.2.2.3.2.1" xref="S2.p2.3.m1.1.2.2.cmml">(</mo><mi id="S2.p2.3.m1.1.1" xref="S2.p2.3.m1.1.1.cmml">x</mi><mo stretchy="false" id="S2.p2.3.m1.1.2.2.3.2.2" xref="S2.p2.3.m1.1.2.2.cmml">)</mo></mrow></mrow><mo id="S2.p2.3.m1.1.2.1" xref="S2.p2.3.m1.1.2.1.cmml">=</mo><msub id="S2.p2.3.m1.1.2.3" xref="S2.p2.3.m1.1.2.3.cmml"><mi id="S2.p2.3.m1.1.2.3.2" xref="S2.p2.3.m1.1.2.3.2.cmml">V</mi><mn id="S2.p2.3.m1.1.2.3.3" xref="S2.p2.3.m1.1.2.3.3.cmml">0</mn></msub></mrow></math>, <math><mrow id="S2.Ex2.m1.4.4.1" xref="S2.Ex2.m1.4.4.1.1.cmml"><mrow id="S2.Ex2.m1.4.4.1.1" xref="S2.Ex2.m1.4.4.1.1.cmml"><mrow id="S2.Ex2.m1.4.4.1.1.2" xref="S2.Ex2.m1.4.4.1.1.2.cmml"><mrow id="S2.Ex2.m1.4.4.1.1.2.2" xref="S2.Ex2.m1.4.4.1.1.2.2.cmml"><mo id="S2.Ex2.m1.4.4.1.1.2.2.1" xref="S2.Ex2.m1.4.4.1.1.2.2.1.cmml">-</mo><mrow id="S2.Ex2.m1.4.4.1.1.2.2.2" xref="S2.Ex2.m1.4.4.1.1.2.2.2.cmml"><mfrac id="S2.Ex2.m1.4.4.1.1.2.2.2.2" xref="S2.Ex2.m1.4.4.1.1.2.2.2.2.cmml"><msup id="S2.Ex2.m1.4.4.1.1.2.2.2.2.2" xref="S2.Ex2.m1.4.4.1.1.2.2.2.2.2.cmml"><mi mathvariant="normal" id="S2.Ex2.m1.4.4.1.1.2.2.2.2.2.2" xref="S2.Ex2.m1.4.4.1.1.2.2.2.2.2.2.cmml">ℏ</mi><mn id="S2.Ex2.m1.4.4.1.1.2.2.2.2.2.3" xref="S2.Ex2.m1.4.4.1.1.2.2.2.2.2.3.cmml">2</mn></msup><mrow id="S2.Ex2.m1.4.4.1.1.2.2.2.2.3" xref="S2.Ex2.m1.4.4.1.1.2.2.2.2.3.cmml"><mn id="S2.Ex2.m1.4.4.1.1.2.2.2.2.3.2" xref="S2.Ex2.m1.4.4.1.1.2.2.2.2.3.2.cmml">2</mn><mo id="S2.Ex2.m1.4.4.1.1.2.2.2.2.3.1" xref="S2.Ex2.m1.4.4.1.1.2.2.2.2.3.1.cmml">⁢</mo><mi id="S2.Ex2.m1.4.4.1.1.2.2.2.2.3.3" xref="S2.Ex2.m1.4.4.1.1.2.2.2.2.3.3.cmml">m</mi></mrow></mfrac><mo id="S2.Ex2.m1.4.4.1.1.2.2.2.1" xref="S2.Ex2.m1.4.4.1.1.2.2.2.1.cmml">⁢</mo><mfrac id="S2.Ex2.m1.1.1" xref="S2.Ex2.m1.1.1.cmml"><mrow id="S2.Ex2.m1.1.1.1" xref="S2.Ex2.m1.1.1.1.cmml"><msup id="S2.Ex2.m1.1.1.1.3" xref="S2.Ex2.m1.1.1.1.3.cmml"><mi id="S2.Ex2.m1.1.1.1.3.2" xref="S2.Ex2.m1.1.1.1.3.2.cmml">d</mi><mn id="S2.Ex2.m1.1.1.1.3.3" xref="S2.Ex2.m1.1.1.1.3.3.cmml">2</mn></msup><mo id="S2.Ex2.m1.1.1.1.2" xref="S2.Ex2.m1.1.1.1.2.cmml">⁢</mo><mi id="S2.Ex2.m1.1.1.1.4" xref="S2.Ex2.m1.1.1.1.4.cmml">ϕ</mi><mo id="S2.Ex2.m1.1.1.1.2a" xref="S2.Ex2.m1.1.1.1.2.cmml">⁢</mo><mrow id="S2.Ex2.m1.1.1.1.5.2" xref="S2.Ex2.m1.1.1.1.cmml"><mo stretchy="false" id="S2.Ex2.m1.1.1.1.5.2.1" xref="S2.Ex2.m1.1.1.1.cmml">(</mo><mn id="S2.Ex2.m1.1.1.1.1" xref="S2.Ex2.m1.1.1.1.1.cmml">0</mn><mo stretchy="false" id="S2.Ex2.m1.1.1.1.5.2.2" xref="S2.Ex2.m1.1.1.1.cmml">)</mo></mrow></mrow><mrow id="S2.Ex2.m1.1.1.3" xref="S2.Ex2.m1.1.1.3.cmml"><mi id="S2.Ex2.m1.1.1.3.2" xref="S2.Ex2.m1.1.1.3.2.cmml">d</mi><mo id="S2.Ex2.m1.1.1.3.1" xref="S2.Ex2.m1.1.1.3.1.cmml">⁢</mo><msup id="S2.Ex2.m1.1.1.3.3" xref="S2.Ex2.m1.1.1.3.3.cmml"><mi id="S2.Ex2.m1.1.1.3.3.2" xref="S2.Ex2.m1.1.1.3.3.2.cmml">x</mi><mn id="S2.Ex2.m1.1.1.3.3.3" xref="S2.Ex2.m1.1.1.3.3.3.cmml">2</mn></msup></mrow></mfrac></mrow></mrow><mo id="S2.Ex2.m1.4.4.1.1.2.1" xref="S2.Ex2.m1.4.4.1.1.2.1.cmml">-</mo><mrow id="S2.Ex2.m1.4.4.1.1.2.3" xref="S2.Ex2.m1.4.4.1.1.2.3.cmml"><msub id="S2.Ex2.m1.4.4.1.1.2.3.2" xref="S2.Ex2.m1.4.4.1.1.2.3.2.cmml"><mi id="S2.Ex2.m1.4.4.1.1.2.3.2.2" xref="S2.Ex2.m1.4.4.1.1.2.3.2.2.cmml">V</mi><mn id="S2.Ex2.m1.4.4.1.1.2.3.2.3" xref="S2.Ex2.m1.4.4.1.1.2.3.2.3.cmml">0</mn></msub><mo id="S2.Ex2.m1.4.4.1.1.2.3.1" xref="S2.Ex2.m1.4.4.1.1.2.3.1.cmml">⁢</mo><mi id="S2.Ex2.m1.4.4.1.1.2.3.3" xref="S2.Ex2.m1.4.4.1.1.2.3.3.cmml">ϕ</mi><mo id="S2.Ex2.m1.4.4.1.1.2.3.1a" xref="S2.Ex2.m1.4.4.1.1.2.3.1.cmml">⁢</mo><mrow id="S2.Ex2.m1.4.4.1.1.2.3.4.2" xref="S2.Ex2.m1.4.4.1.1.2.3.cmml"><mo stretchy="false" id="S2.Ex2.m1.4.4.1.1.2.3.4.2.1" xref="S2.Ex2.m1.4.4.1.1.2.3.cmml">(</mo><mn id="S2.Ex2.m1.2.2" xref="S2.Ex2.m1.2.2.cmml">0</mn><mo stretchy="false" id="S2.Ex2.m1.4.4.1.1.2.3.4.2.2" xref="S2.Ex2.m1.4.4.1.1.2.3.cmml">)</mo></mrow></mrow></mrow><mo id="S2.Ex2.m1.4.4.1.1.1" xref="S2.Ex2.m1.4.4.1.1.1.cmml">=</mo><mrow id="S2.Ex2.m1.4.4.1.1.3" xref="S2.Ex2.m1.4.4.1.1.3.cmml"><mi id="S2.Ex2.m1.4.4.1.1.3.2" xref="S2.Ex2.m1.4.4.1.1.3.2.cmml">E</mi><mo id="S2.Ex2.m1.4.4.1.1.3.1" xref="S2.Ex2.m1.4.4.1.1.3.1.cmml">⁢</mo><mi id="S2.Ex2.m1.4.4.1.1.3.3" xref="S2.Ex2.m1.4.4.1.1.3.3.cmml">ϕ</mi><mo id="S2.Ex2.m1.4.4.1.1.3.1a" xref="S2.Ex2.m1.4.4.1.1.3.1.cmml">⁢</mo><mrow id="S2.Ex2.m1.4.4.1.1.3.4.2" xref="S2.Ex2.m1.4.4.1.1.3.cmml"><mo stretchy="false" id="S2.Ex2.m1.4.4.1.1.3.4.2.1" xref="S2.Ex2.m1.4.4.1.1.3.cmml">(</mo><mn id="S2.Ex2.m1.3.3" xref="S2.Ex2.m1.3.3.cmml">0</mn><mo stretchy="false" id="S2.Ex2.m1.4.4.1.1.3.4.2.2" xref="S2.Ex2.m1.4.4.1.1.3.cmml">)</mo></mrow></mrow></mrow><mo id="S2.Ex2.m1.4.4.1.2" xref="S2.Ex2.m1.4.4.1.1.cmml">.</mo></mrow></math>, <math><mrow id="S2.Ex3.m1.1.1.1" xref="S2.Ex3.m1.1.1.1.1.cmml"><mrow id="S2.Ex3.m1.1.1.1.1" xref="S2.Ex3.m1.1.1.1.1.cmml"><mrow id="S2.Ex3.m1.1.1.1.1.2" xref="S2.Ex3.m1.1.1.1.1.2.cmml"><mo id="S2.Ex3.m1.1.1.1.1.2.1" xref="S2.Ex3.m1.1.1.1.1.2.1.cmml">-</mo><mrow id="S2.Ex3.m1.1.1.1.1.2.2" xref="S2.Ex3.m1.1.1.1.1.2.2.cmml"><mfrac id="S2.Ex3.m1.1.1.1.1.2.2.2" xref="S2.Ex3.m1.1.1.1.1.2.2.2.cmml"><msup id="S2.Ex3.m1.1.1.1.1.2.2.2.2" xref="S2.Ex3.m1.1.1.1.1.2.2.2.2.cmml"><mi mathvariant="normal" id="S2.Ex3.m1.1.1.1.1.2.2.2.2.2" xref="S2.Ex3.m1.1.1.1.1.2.2.2.2.2.cmml">ℏ</mi><mn id="S2.Ex3.m1.1.1.1.1.2.2.2.2.3" xref="S2.Ex3.m1.1.1.1.1.2.2.2.2.3.cmml">2</mn></msup><mrow id="S2.Ex3.m1.1.1.1.1.2.2.2.3" xref="S2.Ex3.m1.1.1.1.1.2.2.2.3.cmml"><mn id="S2.Ex3.m1.1.1.1.1.2.2.2.3.2" xref="S2.Ex3.m1.1.1.1.1.2.2.2.3.2.cmml">2</mn><mo id="S2.Ex3.m1.1.1.1.1.2.2.2.3.1" xref="S2.Ex3.m1.1.1.1.1.2.2.2.3.1.cmml">⁢</mo><mi id="S2.Ex3.m1.1.1.1.1.2.2.2.3.3" xref="S2.Ex3.m1.1.1.1.1.2.2.2.3.3.cmml">m</mi></mrow></mfrac><mo id="S2.Ex3.m1.1.1.1.1.2.2.1" xref="S2.Ex3.m1.1.1.1.1.2.2.1.cmml">⁢</mo><mfrac id="S2.Ex3.m1.1.1.1.1.2.2.3" xref="S2.Ex3.m1.1.1.1.1.2.2.3.cmml"><mrow id="S2.Ex3.m1.1.1.1.1.2.2.3.2" xref="S2.Ex3.m1.1.1.1.1.2.2.3.2.cmml"><msup id="S2.Ex3.m1.1.1.1.1.2.2.3.2.2" xref="S2.Ex3.m1.1.1.1.1.2.2.3.2.2.cmml"><mi id="S2.Ex3.m1.1.1.1.1.2.2.3.2.2.2" xref="S2.Ex3.m1.1.1.1.1.2.2.3.2.2.2.cmml">d</mi><mn id="S2.Ex3.m1.1.1.1.1.2.2.3.2.2.3" xref="S2.Ex3.m1.1.1.1.1.2.2.3.2.2.3.cmml">2</mn></msup><mo id="S2.Ex3.m1.1.1.1.1.2.2.3.2.1" xref="S2.Ex3.m1.1.1.1.1.2.2.3.2.1.cmml">⁢</mo><mi id="S2.Ex3.m1.1.1.1.1.2.2.3.2.3" xref="S2.Ex3.m1.1.1.1.1.2.2.3.2.3.cmml">ϕ</mi></mrow><mrow id="S2.Ex3.m1.1.1.1.1.2.2.3.3" xref="S2.Ex3.m1.1.1.1.1.2.2.3.3.cmml"><mi id="S2.Ex3.m1.1.1.1.1.2.2.3.3.2" xref="S2.Ex3.m1.1.1.1.1.2.2.3.3.2.cmml">d</mi><mo id="S2.Ex3.m1.1.1.1.1.2.2.3.3.1" xref="S2.Ex3.m1.1.1.1.1.2.2.3.3.1.cmml">⁢</mo><msup id="S2.Ex3.m1.1.1.1.1.2.2.3.3.3" xref="S2.Ex3.m1.1.1.1.1.2.2.3.3.3.cmml"><mi id="S2.Ex3.m1.1.1.1.1.2.2.3.3.3.2" xref="S2.Ex3.m1.1.1.1.1.2.2.3.3.3.2.cmml">x</mi><mn id="S2.Ex3.m1.1.1.1.1.2.2.3.3.3.3" xref="S2.Ex3.m1.1.1.1.1.2.2.3.3.3.3.cmml">2</mn></msup></mrow></mfrac></mrow></mrow><mo id="S2.Ex3.m1.1.1.1.1.1" xref="S2.Ex3.m1.1.1.1.1.1.cmml">=</mo><mrow id="S2.Ex3.m1.1.1.1.1.3" xref="S2.Ex3.m1.1.1.1.1.3.cmml"><mi id="S2.Ex3.m1.1.1.1.1.3.2" xref="S2.Ex3.m1.1.1.1.1.3.2.cmml">E</mi><mo id="S2.Ex3.m1.1.1.1.1.3.1" xref="S2.Ex3.m1.1.1.1.1.3.1.cmml">⁢</mo><mi id="S2.Ex3.m1.1.1.1.1.3.3" xref="S2.Ex3.m1.1.1.1.1.3.3.cmml">ϕ</mi></mrow></mrow><mo id="S2.Ex3.m1.1.1.1.2" xref="S2.Ex3.m1.1.1.1.1.cmml">.</mo></mrow></math>, <math><mrow id="S2.Ex4.m1.3.4" xref="S2.Ex4.m1.3.4.cmml"><mi id="S2.Ex4.m1.3.4.2" xref="S2.Ex4.m1.3.4.2.cmml">ϕ</mi><mo id="S2.Ex4.m1.3.4.1" xref="S2.Ex4.m1.3.4.1.cmml">=</mo><mrow id="S2.Ex4.m1.3.3" xref="S2.Ex4.m1.3.4.3.1.cmml"><mo id="S2.Ex4.m1.3.3.4" xref="S2.Ex4.m1.3.4.3.1.1.cmml">{</mo><mtable columnspacing="5pt" displaystyle="true" rowspacing="0pt" id="S2.Ex4.m1.3.3.3" xref="S2.Ex4.m1.3.4.3.1.cmml"><mtr id="S2.Ex4.m1.3.3.3a" xref="S2.Ex4.m1.3.4.3.1.cmml"><mtd columnalign="left" id="S2.Ex4.m1.3.3.3b" xref="S2.Ex4.m1.3.4.3.1.cmml"><mrow id="S2.Ex4.m1.1.1.1.1.1.1" xref="S2.Ex4.m1.1.1.1.1.1.1.cmml"><mrow id="S2.Ex4.m1.1.1.1.1.1.1.2.1" xref="S2.Ex4.m1.1.1.1.1.1.1.2.2.cmml"><mrow id="S2.Ex4.m1.1.1.1.1.1.1.2.1.1" xref="S2.Ex4.m1.1.1.1.1.1.1.2.1.1.cmml"><mi id="S2.Ex4.m1.1.1.1.1.1.1.2.1.1.2" xref="S2.Ex4.m1.1.1.1.1.1.1.2.1.1.2.cmml">A</mi><mo id="S2.Ex4.m1.1.1.1.1.1.1.2.1.1.1" xref="S2.Ex4.m1.1.1.1.1.1.1.2.1.1.1.cmml">⁢</mo><msup id="S2.Ex4.m1.1.1.1.1.1.1.2.1.1.3" xref="S2.Ex4.m1.1.1.1.1.1.1.2.1.1.3.cmml"><mi id="S2.Ex4.m1.1.1.1.1.1.1.2.1.1.3.2" xref="S2.Ex4.m1.1.1.1.1.1.1.2.1.1.3.2.cmml">e</mi><mrow id="S2.Ex4.m1.1.1.1.1.1.1.2.1.1.3.3" xref="S2.Ex4.m1.1.1.1.1.1.1.2.1.1.3.3.cmml"><mi id="S2.Ex4.m1.1.1.1.1.1.1.2.1.1.3.3.2" xref="S2.Ex4.m1.1.1.1.1.1.1.2.1.1.3.3.2.cmml">κ</mi><mo id="S2.Ex4.m1.1.1.1.1.1.1.2.1.1.3.3.1" xref="S2.Ex4.m1.1.1.1.1.1.1.2.1.1.3.3.1.cmml">⁢</mo><mi id="S2.Ex4.m1.1.1.1.1.1.1.2.1.1.3.3.3" xref="S2.Ex4.m1.1.1.1.1.1.1.2.1.1.3.3.3.cmml">x</mi></mrow></msup></mrow><mo separator="true" id="S2.Ex4.m1.1.1.1.1.1.1.2.1.2" xref="S2.Ex4.m1.1.1.1.1.1.1.2.2.cmml">    </mo><mi id="S2.Ex4.m1.1.1.1.1.1.1.1" xref="S2.Ex4.m1.1.1.1.1.1.1.1.cmml">x</mi></mrow><mo id="S2.Ex4.m1.1.1.1.1.1.1.3" xref="S2.Ex4.m1.1.1.1.1.1.1.3.cmml"><</mo><mrow id="S2.Ex4.m1.1.1.1.1.1.1.4" xref="S2.Ex4.m1.1.1.1.1.1.1.4.cmml"><mo id="S2.Ex4.m1.1.1.1.1.1.1.4.1" xref="S2.Ex4.m1.1.1.1.1.1.1.4.1.cmml">-</mo><mrow id="S2.Ex4.m1.1.1.1.1.1.1.4.2" xref="S2.Ex4.m1.1.1.1.1.1.1.4.2.cmml"><mrow id="S2.Ex4.m1.1.1.1.1.1.1.4.2.2" xref="S2.Ex4.m1.1.1.1.1.1.1.4.2.2.cmml"><mi id="S2.Ex4.m1.1.1.1.1.1.1.4.2.2.2" xref="S2.Ex4.m1.1.1.1.1.1.1.4.2.2.2.cmml">δ</mi><mo id="S2.Ex4.m1.1.1.1.1.1.1.4.2.2.1" xref="S2.Ex4.m1.1.1.1.1.1.1.4.2.2.1.cmml">⁢</mo><mi id="S2.Ex4.m1.1.1.1.1.1.1.4.2.2.3" xref="S2.Ex4.m1.1.1.1.1.1.1.4.2.2.3.cmml">x</mi></mrow><mo id="S2.Ex4.m1.1.1.1.1.1.1.4.2.1" xref="S2.Ex4.m1.1.1.1.1.1.1.4.2.1.cmml">/</mo><mn id="S2.Ex4.m1.1.1.1.1.1.1.4.2.3" xref="S2.Ex4.m1.1.1.1.1.1.1.4.2.3.cmml">2</mn></mrow></mrow></mrow></mtd><mtd id="S2.Ex4.m1.3.3.3c" xref="S2.Ex4.m1.3.4.3.1.1.cmml"/></mtr><mtr id="S2.Ex4.m1.3.3.3d" xref="S2.Ex4.m1.3.4.3.1.cmml"><mtd columnalign="left" id="S2.Ex4.m1.3.3.3e" xref="S2.Ex4.m1.3.4.3.1.cmml"><mrow id="S2.Ex4.m1.2.2.2.2.1.1" xref="S2.Ex4.m1.2.2.2.2.1.1.cmml"><mrow id="S2.Ex4.m1.2.2.2.2.1.1.3.1" xref="S2.Ex4.m1.2.2.2.2.1.1.3.2.cmml"><mrow id="S2.Ex4.m1.2.2.2.2.1.1.3.1.1" xref="S2.Ex4.m1.2.2.2.2.1.1.3.1.1.cmml"><mi id="S2.Ex4.m1.2.2.2.2.1.1.3.1.1.2" xref="S2.Ex4.m1.2.2.2.2.1.1.3.1.1.2.cmml">ϕ</mi><mo id="S2.Ex4.m1.2.2.2.2.1.1.3.1.1.1" xref="S2.Ex4.m1.2.2.2.2.1.1.3.1.1.1.cmml">⁢</mo><mrow id="S2.Ex4.m1.2.2.2.2.1.1.3.1.1.3.2" xref="S2.Ex4.m1.2.2.2.2.1.1.3.1.1.cmml"><mo stretchy="false" id="S2.Ex4.m1.2.2.2.2.1.1.3.1.1.3.2.1" xref="S2.Ex4.m1.2.2.2.2.1.1.3.1.1.cmml">(</mo><mn id="S2.Ex4.m1.2.2.2.2.1.1.1" xref="S2.Ex4.m1.2.2.2.2.1.1.1.cmml">0</mn><mo stretchy="false" id="S2.Ex4.m1.2.2.2.2.1.1.3.1.1.3.2.2" xref="S2.Ex4.m1.2.2.2.2.1.1.3.1.1.cmml">)</mo></mrow></mrow><mo separator="true" id="S2.Ex4.m1.2.2.2.2.1.1.3.1.2" xref="S2.Ex4.m1.2.2.2.2.1.1.3.2.cmml">  </mo><mi id="S2.Ex4.m1.2.2.2.2.1.1.2" xref="S2.Ex4.m1.2.2.2.2.1.1.2.cmml">x</mi></mrow><mo id="S2.Ex4.m1.2.2.2.2.1.1.6" xref="S2.Ex4.m1.2.2.2.2.1.1.6.cmml">∈</mo><mrow id="S2.Ex4.m1.2.2.2.2.1.1.5.2" xref="S2.Ex4.m1.2.2.2.2.1.1.5.3.cmml"><mo stretchy="false" id="S2.Ex4.m1.2.2.2.2.1.1.5.2.3" xref="S2.Ex4.m1.2.2.2.2.1.1.5.3.cmml">(</mo><mrow id="S2.Ex4.m1.2.2.2.2.1.1.4.1.1" xref="S2.Ex4.m1.2.2.2.2.1.1.4.1.1.cmml"><mo id="S2.Ex4.m1.2.2.2.2.1.1.4.1.1.1" xref="S2.Ex4.m1.2.2.2.2.1.1.4.1.1.1.cmml">-</mo><mrow id="S2.Ex4.m1.2.2.2.2.1.1.4.1.1.2" xref="S2.Ex4.m1.2.2.2.2.1.1.4.1.1.2.cmml"><mrow id="S2.Ex4.m1.2.2.2.2.1.1.4.1.1.2.2" xref="S2.Ex4.m1.2.2.2.2.1.1.4.1.1.2.2.cmml"><mi id="S2.Ex4.m1.2.2.2.2.1.1.4.1.1.2.2.2" xref="S2.Ex4.m1.2.2.2.2.1.1.4.1.1.2.2.2.cmml">δ</mi><mo id="S2.Ex4.m1.2.2.2.2.1.1.4.1.1.2.2.1" xref="S2.Ex4.m1.2.2.2.2.1.1.4.1.1.2.2.1.cmml">⁢</mo><mi id="S2.Ex4.m1.2.2.2.2.1.1.4.1.1.2.2.3" xref="S2.Ex4.m1.2.2.2.2.1.1.4.1.1.2.2.3.cmml">x</mi></mrow><mo id="S2.Ex4.m1.2.2.2.2.1.1.4.1.1.2.1" xref="S2.Ex4.m1.2.2.2.2.1.1.4.1.1.2.1.cmml">/</mo><mn id="S2.Ex4.m1.2.2.2.2.1.1.4.1.1.2.3" xref="S2.Ex4.m1.2.2.2.2.1.1.4.1.1.2.3.cmml">2</mn></mrow></mrow><mo id="S2.Ex4.m1.2.2.2.2.1.1.5.2.4" 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xref="S2.Ex4.m1.3.4.3.1.cmml">.</mo></mrow></mtd><mtd id="S2.Ex4.m1.3.3.3i" xref="S2.Ex4.m1.3.4.3.1.1.cmml"/></mtr></mtable></mrow></mrow></math>

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/0903.3325

Formulas:

1-

\dot{q} = 𝒇 (q, u)

2-

\dot{q} = 𝒇 (q, u), q \in M, u \in U,

3-

\frac{\partial 𝒇 (q, u)}{\partial u} \land \frac{\partial {}^{2}𝒇 (q, u)}{\partial u^{2}} \neq 0, \forall (q, u) \in M \times U .

4-

(q, u) \to (ϕ (q), ψ (q, u))

5-

π : T^{*} M \to M

6-

s_{λ} = λ \circ π_{*}

7-

λ \in T^{*} M

8-

\dot{q} = 𝒇 (q, u), q \in M, u \in U

9-

q (0) \in N_{0}, q (t_{1}) \in N_{1},

10-

t_{1} \to \min (or \max),

Formulas (html):

Correct Categorie: math

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1307.1346

Formulas:

1-

β \equiv P_{g a s} / P_{m a g}

2-

P_{m a g}

3-

P_{g a s}

4-

M_{A} \equiv ⟨ | 𝒗 | / v_{A} ⟩,

5-

v_{A} = | 𝑩 | / \sqrt{ρ}

6-

\frac{d 𝒖}{d t} = \frac{q}{m c} 𝒖 \times 𝑩,

7-

r_{L} = \frac{u}{Ω} .

8-

Ω = \frac{e B}{γ m c},

9-

(μ - μ_{0})

10-

D_{μ μ} = \frac{⟨ {(μ - μ_{0})}^{2} ⟩}{2 t},

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/9805241

Formulas:

1-

σ_{S} = σ / \sqrt{N - 1}

2-

S = S_{0} ν^{α}

3-

- 5^{\circ} \leq b \leq + 5^{\circ}

4-

260^{\circ} \leq l \leq 20^{\circ}

5-

τ_{s c a t t}

6-

τ_{s c a t t}

7-

L = γ P^{α} {\dot{P}}^{β}

8-

σ_{l o g L}

9-

σ_{l o g L}

10-

260^{\circ} \leq l \leq 20^{\circ}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0511585

Formulas:

1-

P_{1} / P_{0} = 0.743

2-

α_{2000} = 15^{h} 46^{m} 26^{s}

3-

δ_{2000} = + 44^{o} 18^{'} 45^{''}

4-

V (5222076) - V (c o m p s t a r)

5-

A 0 / A 1

6-

A 0 / A 1

7-

A 0 / A 1

8-

A 0 / A 1

9-

A 0 / A 1

10-

A 0 / A 1

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1909.11523

Formulas:

1-

α_{i j} \leq π / 2

2-

0 < α_{i j} \leq π / 2

3-

F_{i j k}

4-

α_{i j} + α_{j k} + α_{k i} \geq π

5-

F_{i j k l}

6-

α_{i j} + α_{j k} + α_{k l} + α_{l i} = 2 π

7-

α_{i j} + α_{j k} + α_{k i} < π

8-

α_{i j} + α_{j k} + α_{k l} + α_{l i} < 2 π

9-

α_{13} + α_{14} + α_{15} + α_{23} + α_{24} + α_{25} < 3 π

10-

α_{i j} + α_{j k} < π

Formulas (html):

Correct Categorie: math

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/nlin/0006016

Formulas:

1-

S U (2)

2-

A f (1)

3-

g = (\begin{matrix} a & b \\ 0 & 1 \end{matrix}), a > 0, b \in 𝐑 .

4-

A f (1)

5-

a = \exp (θ_{1}), b = θ_{2}

6-

c_{12}^{2} = - c_{21}^{2} = 1

7-

J_{μ} := g^{- 1} \partial_{μ} g

8-

(\partial_{μ} θ_{1}, e^{- θ_{1}} \partial_{μ} θ_{2})

9-

I [g] = \int d^{2} x η^{μ ν} L (J_{μ}, J_{ν}),

10-

J_{μ} := (g^{- 1} \partial_{μ} g) \in ℒ (G),

Formulas (html):

Correct Categorie: nlin

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/nucl-th/9811030

Formulas:

1-

Δ ω / ω \sim A^{- 4 / 3}

2-

Δ ω / ω \sim A^{- 4 / 3}

3-

Δ ω / ω \sim 1 / m_{e}^{4} L^{4}

4-

R \sim A^{1 / 3}

5-

Δ ω / ω \sim R^{- 4}

6-

H = \frac{1}{2} ϵ σ_{z} - \frac{V}{2} σ_{x} σ_{x} .

7-

\sum_{i = 1}^{N} (a_{1 i}^{†} a_{1 i} - a_{0 i}^{†} a_{0 i}),

8-

\sum_{i = 1}^{N} (a_{1 i}^{†} a_{0 i} + a_{0 i}^{†} a_{1 i}),

9-

< 0 | σ_{i} | 0 > = - N δ_{i, z} .

10-

O^{†} = X (\sum_{i = 1}^{N} a_{1 i}^{†} a_{0 i}) - Y (\sum_{i = 1}^{N} a_{0 i}^{†} a_{1 i}),

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/quant-ph/0205058

Formulas:

1-

A (d s_{1} + d s_{2}) = A (d s_{1}) A (d s_{2}) .

2-

A (d s) = \exp (z d s)

3-

A (s [𝒞]) = \exp (z s [𝒞])

4-

A (s [𝒞])

5-

\exp (i b s [𝒞])

6-

(x_{1}, t_{1})

7-

(x_{2}, t_{2})

8-

K (x_{2}, t_{2}; x_{1}, t_{1})

9-

(x_{2}, t_{2})

10-

(x_{1}, t_{1})

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/2012.14908

Formulas:

1-

H = - J \sum_{i > j} \frac{{(- 1)}^{| x_{i} + y_{i} - x_{j} - y_{j} |}}{{| {\vec{r}}_{i} - {\vec{r}}_{j} |}^{α}} {\vec{S}}_{i} \cdot {\vec{S}}_{j} .

2-

\vec{r_{i}} = (x_{i}, y_{i})

3-

y_{i} = 1, 2

4-

J_{r u n g} \to \infty

5-

O = - lim_{l \to \infty} ⟨ {\tilde{S}}_{0}^{z} (\prod_{j = 1}^{l - 1} e^{i π {\tilde{S}}_{j}^{z}}) {\tilde{S}}_{l}^{z} ⟩,

6-

{\tilde{S}}_{j}^{z} = S_{j + 1, 1}^{z} + S_{j, 2}^{z}

7-

S^{z} (q, ω)

8-

α_{c} = 2.09 (3)

9-

S_{π} = \frac{1}{L} \sum_{r} {(- 1)}^{x + y} ⟨ S_{0}^{z} S_{r}^{z} ⟩,

10-

S_{π} = L^{- \frac{β}{ν}} f ((α - α_{c}) L^{\frac{1}{ν}}),

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1904.01801

Formulas:

1-

= ω_{1}^{i} + λ_{+} \sum_{j = 1}^{N} A_{1}^{i j} [\sin (θ_{1}^{j} - θ_{1}^{i})] + D_{x} [\sin (θ_{2}^{i} - θ_{1}^{i})],

2-

= ω_{2}^{i} + λ_{-} \sum_{j = 1}^{N} A_{2}^{i j} [\sin (θ_{2}^{j} - θ_{2}^{i})] + D_{x} [\sin (θ_{1}^{i} - θ_{2}^{i})],

3-

θ^{i} (t)

4-

i = 1, \dots, N

5-

(λ_{+} > 0)

6-

(λ_{-} < 0)

7-

A^{i j} = 1

8-

{𝐀_{1}, 𝐀_{2}, \dots, 𝐀_{M}}

9-

ℳ = (\begin{matrix} 𝐀_{1} & 𝒟_{𝓍} 𝐈 \\ 𝒟_{𝓍} 𝐈 & 𝐀_{2} \end{matrix})

10-

r_{1} (t) e^{ı ϕ_{1}}

Formulas (html):

Correct Categorie: nlin

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1007.0314

Formulas:

1-

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

2-

{| Ψ ⟩}_{SP} = \frac{1}{\sqrt{2}} ({| 0 ⟩}_{S} {| 0 ⟩}_{P} \pm {| 1 ⟩}_{S} {| 1 ⟩}_{P})

3-

{| Ψ ⟩}_{SP} = \frac{1}{\sqrt{2}} ({| 0 ⟩}_{S} {| 1 ⟩}_{P} \pm {| 1 ⟩}_{S} {| 0 ⟩}_{P})

4-

{\hat{ρ}}_{S} = \frac{1}{2} ({| 0 ⟩}_{S} ⟨ 0 | + {| 1 ⟩}_{S} ⟨ 1 |)

5-

{| \pm ⟩}_{S} \to {| \mp ⟩}_{S}

6-

{| ψ ⟩}_{S} = \int 𝑑 x ψ (x) {| x ⟩}_{S}

7-

\hat{U} = \exp (i {\hat{x}}_{S} {\hat{p}}_{P} / ℏ)

8-

{| x = 0 ⟩}_{P}

9-

{| Ψ ⟩}_{SP} = \int 𝑑 x ψ (x) {| x ⟩}_{S} {| x ⟩}_{P}

10-

{\hat{ρ}}_{S} = \int 𝑑 x {| ψ (x) |}^{2} {| x ⟩}_{S} ⟨ x |

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/1809.03491

Formulas:

1-

e_{α} = - \bar{J} (S_{B} \cdot S + S_{B} \cdot S^{'}) - {\bar{J}}_{P} \cdot S \cdot S^{'} - \bar{J^{'}} \cdot S_{B} \cdot S \cdot S^{'} - H (S + S_{B}),

2-

Z_{B} (S_{B})

3-

Z_{m} (+) = \sum_{Γ = 1}^{4} Z_{m + 1} (S_{m + 1}) Z_{B} (S_{B}) w (Γ),

4-

Z_{m} (-) = \sum_{Γ = 5}^{4} Z_{m + 1} (S_{m + 1}) Z_{B} (S_{B}) w (Γ),

5-

{\bar{x}}_{m} = \frac{Z_{m} (+)}{Z_{m} (+) + Z_{m} (-)}, {\bar{y}}_{m} = \frac{Z_{m} (-)}{Z_{m} (+) + Z_{m} (-)}

6-

{\bar{z}}_{m} (S_{m}) = {\begin{matrix} {\bar{x}}_{m} if S_{m} = + 1 \\ {\bar{y}}_{m} if S_{m} = - 1 \end{matrix},

7-

Z_{m} (+) = B_{m} {\bar{x}}_{m}

8-

Z_{m} (-) = B_{m} {\bar{y}}_{m}

9-

B_{m} = Z_{m} (+) + Z_{m} (-)

10-

{\bar{z}}_{m} (S_{m}) = \frac{B_{m + 1}^{2} B_{B}}{B_{m}} \sum_{Γ} {\bar{z}}_{m + 1} (S_{m + 1}) z_{B} (S_{B}) w (Γ),

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/cond-mat/0612651

Formulas:

1-

g ≪ 1 ≪ g | \ln ω |

2-

σ = e^{2} / 4 ℏ

3-

\bar{σ} = 2 e^{2} / π^{2} ℏ

4-

e^{2} / 16 ℏ

5-

H = v_{0} \sum_{i 𝐩} {\hat{c}}_{𝐩}^{i, †} \hat{𝝈} \cdot 𝐩 {\hat{c}}_{𝐩}^{i} + \frac{1}{2} \sum_{i j 𝐩𝐤𝐪} {\hat{c}}_{𝐩 - 𝐪}^{i, †} {\hat{c}}_{𝐤 + 𝐪}^{j, †} V_{𝐪} {\hat{c}}_{𝐤}^{j} {\hat{c}}_{𝐩}^{i},

6-

V_{𝐪} = 2 π e^{2} / κ | 𝐪 |

7-

\sum_{𝐩} \equiv \int d^{2} p / {(2 π)}^{2}

8-

g = e^{2} / κ v_{0}

9-

{\hat{G}}_{ϵ 𝐩} = \frac{1}{ϵ - v_{0} p {\hat{σ}}_{𝐩} + i η sgn ϵ} = \frac{1}{2} \sum_{β = \pm 1} \frac{1 + β {\hat{σ}}_{𝐩}}{ϵ - β (v_{0} p - i η)},

10-

{\hat{σ}}_{𝐩} = \hat{𝝈} \cdot 𝐧

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/quant-ph/0007056

Formulas:

1-

H_{1} = 2 κ J_{z}^{2},

2-

H_{2} = i κ (J_{+}^{2} - J_{-}^{2}) .

3-

H_{3} = 2 κ J_{z}^{2} + Ω J_{x} .

4-

ξ_{s} = \frac{\sqrt{2} ⟨ {(Δ J_{⊥})}_{m i n} ⟩}{J^{1 / 2}},

5-

⟨ {(Δ J_{⊥})}_{m i n} ⟩

6-

| J, m_{x} = - J ⟩

7-

2 κ J_{z}^{2}

8-

| J, m_{x} = - J ⟩

9-

| J, m_{x} = - J ⟩

10-

⟨ J_{y} ⟩ = ⟨ J_{y} ⟩ = 0

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/1906.08768

Formulas:

1-

= a_{e}^{EXP} - a_{e}^{SM} = (- 8.7 \pm 3.6) \times 10^{- 13},

2-

= a_{μ}^{EXP} - a_{μ}^{SM} = (27.4 \pm 7.3) \times 10^{- 10},

3-

\frac{Δ a_{e}}{Δ a_{μ}} \sim \frac{m_{e}^{2}}{m_{μ}^{2}} ≃ 2.4 \times 10^{- 5} .

4-

\tan β \equiv ⟨ H_{u}^{0} ⟩ / ⟨ H_{d}^{0} ⟩

5-

y_{i} ≃ \frac{m_{i}}{v} \frac{\sqrt{1 + \tan^{2} β}}{1 + Δ_{i}},

6-

v^{2} = {⟨ H_{u}^{0} ⟩}^{2} + {⟨ H_{d}^{0} ⟩}^{2} ≃ {(174 GeV)}^{2}

7-

Δ_{i} ≃ μ \tan β \frac{g_{Y}^{2} M_{1}}{16 π^{2}} I (M_{1}^{2}, m_{{\tilde{i}}_{L}}^{2}, m_{{\tilde{i}}_{R}}^{2}),

8-

I (x, y, z) = - \frac{x y \ln (x / y) + y z \ln (y / z) + z x \ln (z / x)}{(x - y) (y - z) (z - x)},

9-

I (x, x, x) = 1 / 2 x^{2}

10-

m_{{\tilde{i}}_{L}} = m_{{\tilde{i}}_{R}} = M_{1}

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0704.0826

Formulas:

1-

z_{a b s} = 0.524

2-

τ_{9.7} \approx 0.08 - 0.09

3-

E (B - V)

4-

E (B - V)

5-

z_{a b s} = 0.524

6-

z_{e m} = 0.94

7-

E (B - V)

8-

57 ″ \times 3.6 ″

9-

168 ″ \times 10.5 ″

10-

E (B - V) = 0.23 \pm 0.01

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/math/0611922

Formulas:

1-

C (M) = \int_{M} K

2-

n \in ℕ, n \geq 3

3-

ℛ = {R_{t}}_{t > 0}

4-

(t, 0, 2)

5-

(t, 0, 2)

6-

𝕊^{1} \times ℝ^{2}, ℝ^{3} / S_{θ}, 𝕋^{2} \times ℝ

7-

(2, 0, 0), (0, 2, 0)

8-

(2, 0, 0), (2 \cos θ, 2 \sin θ, 0)

9-

θ \in (0, \frac{π}{2}]

10-

θ \in (0, \frac{π}{2}]

Formulas (html):

Correct Categorie: math

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1408.2815

Formulas:

1-

T_{c} ≃ 500 K

2-

T_{c} ≃ 500 K

3-

F = E - T S

4-

J = 0.7 e V

5-

U = 6 e V

6-

d P / d V

7-

F = E - T S

8-

P = - d F / d V

9-

d P / d V

10-

d P / d V

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0302455

Formulas:

1-

M_{b h} - M_{b u l g e}

2-

M_{b h} - σ

3-

M_{b h} - M_{b u l g e}

4-

M_{b h} - M_{b u l g e}

5-

M_{b h} - M_{b u l g e}

6-

M_{b h} - σ

7-

M_{b h} - σ

8-

M_{b h} - M_{b u l g e}

9-

M_{b h} - M_{b u l g e}

10-

M_{b h} - σ

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1309.3019

Formulas:

1-

𝐣 = \frac{1}{μ} (j_{f}, 0, j_{s p}) .

2-

𝐁 = (x - \frac{j_{s p}}{2} y, \frac{j_{s p}}{2} x + b y, j_{f} y - (b + 1) z),

3-

\frac{\partial ρ}{\partial t} + \nabla \cdot (ρ 𝐯)

4-

ρ \frac{\partial 𝐯}{\partial t} + ρ (𝐯 \cdot \nabla) 𝐯

5-

- \nabla p + (\nabla \times 𝐁) \times 𝐁 + 𝐅_{ν},

6-

\frac{\partial p}{\partial t} + 𝐯 \cdot \nabla p

7-

- γ p \nabla \cdot 𝐯 + H_{ν},

8-

\frac{\partial 𝐁}{\partial t}

9-

\nabla \times (𝐯 \times 𝐁),

10-

p = ρ ϵ (γ - 1)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1009.3973

Formulas:

1-

F_{1}, \dots, F_{k} \in ℱ

2-

\cap_{i = 1}^{k} F_{i} \neq \emptyset

3-

r \leq \frac{(k - 1) n}{k}

4-

| ℱ | \leq (\binom{n - 1}{r - 1})

5-

ℐ^{r} (G)

6-

ℳ^{r} (G)

7-

ℋ^{r} (G) = ℐ^{r} (G) \cup ℳ^{r} (G)

8-

ℋ^{r} (M_{n})

9-

[n] = {1, 2, \dots, n}

10-

[i, j] = {i, i + 1, \dots, j}

Formulas (html):

Correct Categorie: math

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/nucl-th/0401001

Formulas:

1-

3 < p_{T} < 8

2-

3 < p_{T} < 4

3-

4 < p_{T} < 8

4-

d N / p_{T} d p_{T}

5-

d p / p^{0}

6-

p \frac{d N_{M}}{d p} = \int \frac{d p_{1}}{p_{1}} \frac{d p_{2}}{p_{2}} F_{q {\bar{q}}^{'}} (p_{1}, p_{2}) R_{M} (p_{1}, p_{2}, p),

7-

F_{q {\bar{q}}^{'}} (p_{1}, p_{2})

8-

R_{M} (p_{1}, p_{2}, p)

9-

q {\bar{q}}^{'} \to M

10-

R_{M} (p_{1}, p_{2}, p)

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1210.8384

Formulas:

1-

23^{0} 10^{'} N

2-

89^{0} 10^{'} E

3-

30^{0} 27^{'} N

4-

78^{0} 06^{'} E

5-

17^{0} 10^{'} N

6-

70^{0} 20^{'} E

7-

L o g a p e r t u r e i n i n c h e s \times 5 + {9.2}^{''}

8-

L o g 3 \times 5 + 9.2

9-

L o g 6.25 \times 5 + 9.2

10-

N o v a A q u i l a e 1918

Formulas (html):

Correct Categorie: physics

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1206.6035

Formulas:

1-

[- \frac{1}{2} \nabla^{2} + v_{e x t} + v_{H} - E] ψ (𝐫) + \int Σ (𝐫, 𝐫^{'}, E) ψ (𝐫^{'}) 𝑑 𝐫^{'} = 0

2-

v_{e x t}

3-

V_{e x t} + V_{H}

4-

Σ (x, x^{'}) = \frac{f (x) + f (x^{'})}{2} g (| x - x^{'} |)

5-

g (x) = exp (- {(x / w)}^{2}) / \sqrt{π} w

6-

f (x) = - F_{0} [1 - cos (2 π x / a)]

7-

(v_{g} = d E / d k)

8-

⟨ p_{Q P} ⟩ = 0.65 \times 2 π / a

9-

ψ (x, 0) \leftarrow e^{i θ (x, 0)} ψ (x, 0)

10-

n_{Q P} (x, t) = n (x, t) - n_{G S} (x)

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1604.06347

Formulas:

1-

P_{1}, \dots, P_{s}

2-

ℙ^{n} := ℙ_{K}^{n}

3-

℘_{1}, \dots, ℘_{s}

4-

R := K [X_{0}, \dots, X_{n}]

5-

P_{1}, \dots, P_{s}

6-

m_{1}, \dots, m_{s}

7-

m_{1} P_{1} + \dots + m_{s} P_{s}

8-

I := ℘_{1}^{m_{1}} \cap \dots \cap ℘_{s}^{m_{s}}

9-

Z := m_{1} P_{1} + \dots + m_{s} P_{s}

10-

R / I = \underset{t \geq 0}{\oplus} {(R / I)}_{t}

Formulas (html):

Correct Categorie: math

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/9903259

Formulas:

1-

\sim 10^{7 – 8}

2-

\sim 10^{7 – 8}

3-

10^{7 – 8}

4-

τ_{grow} ≃ 5 \times 10^{7}

5-

{[d M_{d} / d t]}_{acc}

6-

{[\frac{d M_{d}}{d t}]}_{acc} = \frac{𝒟 M_{g} (1 - f)}{τ_{acc}},

7-

M_{d} = 𝒟 M_{g}

8-

{[d M_{d} / d t]}_{acc}

9-

{[\frac{d M_{d}}{d t}]}_{acc} = \frac{𝒟 X_{cold} M_{g} (1 - f)}{τ_{grow}},

10-

τ_{acc} = \frac{τ_{grow}}{X_{cold}} .

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0909.0045

Formulas:

1-

Ψ (x, t) = \exp [i S (x, t) / ℏ]

2-

- \frac{\partial S}{\partial t} = \frac{1}{2 m} {(\frac{\partial S}{\partial x})}^{2} + V (x) + \frac{ℏ}{2 m i} \frac{\partial^{2} S}{\partial x^{2}},

3-

S (x, t)

4-

p (x, t) = \partial S (x, t) / \partial x

5-

z = x + i y

6-

\frac{d z}{d t} = \frac{p (z, t)}{m},

7-

p (z, t) = \frac{ℏ}{i} \frac{1}{Ψ (z, t)} \frac{\partial Ψ (z, t)}{\partial z} .

8-

f^{*} (z)

9-

p (z, t) = p_{x} + i p_{y}

10-

𝐏 (z, t) = p_{x} - i p_{y} = (p_{x}, - p_{y})

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/1508.05780

Formulas:

1-

a_{sym}^{*} (A, I)

2-

a_{sym}^{(4)} = 8.33

3-

e_{sym} = a_{sym} I^{2}

4-

I = (N - Z) / A

5-

a_{sym} (A, I) = J - a_{ss} / A^{1 / 3} + a_{sym}^{(4)} I^{2}

6-

a_{sym} (A)

7-

e_{n} (A, I) = e (A, I) - e_{c} (A, I)

8-

e_{n} (A, I)

9-

a_{sym} (A, I)

10-

e (A, I)

Formulas (html):

Correct Categorie: nucl-th

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0902.2189

Formulas:

1-

ξ = \ln (E_{j e t} / p_{h})

2-

E_{j e t}

3-

ξ = \ln (p_{T, j e t} / p_{T, h})

4-

p_{T, j e t}

5-

- 1 < η < 1

6-

Δ η \times Δ ϕ = 0.05 \times 0.05

7-

Δ η \times Δ ϕ = 1 \times 1

8-

R = \sqrt{(Δ ϕ^{2} + Δ η^{2})}

9-

E_{s e e d} = 0.5

10-

f_{s p l i t} = 0.5

Formulas (html):

Correct Categorie: nucl-ex

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0911.5170

Formulas:

1-

M_{*} \sim 0.4 M_{⊙}

2-

a_{W} = a_{S} M_{S} / M_{P}

3-

δ t \sim a_{W} / v_{P}

4-

δ_{T T V} = \frac{1}{\sqrt{2}} \cdot \frac{a_{P}^{1 / 2} a_{S} M_{S} M_{P R V}^{- 1}}{\sqrt{G (M_{*} + M_{P R V})}} \cdot \frac{ζ_{T} (e_{s}, ϖ_{S})}{Υ (e_{P}, ϖ_{P})}

5-

P_{S} \leq P_{P} \sqrt{χ^{3} / 3}

6-

χ_{m a x} ≃ 0.4895

7-

P_{S} \leq 0.2 P_{P}

8-

M_{S} a_{S}^{- 1 / 2}

9-

δ_{T D V} = \sqrt{\frac{a_{P}}{a_{S}}} \sqrt{\frac{M_{S}^{2}}{M_{P R V} (M_{P R V} + M_{*})}} \frac{T}{\sqrt{2}} \frac{ζ_{D} (e_{s}, ϖ_{S})}{Υ (e_{P}, ϖ_{P})}

10-

M_{S} a_{S}^{- 1 / 2}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1406.3517

Formulas:

1-

G (m, 1, n) .

2-

i^{2} = i d_{A}

3-

V \otimes W \to W \otimes V

4-

τ (v \otimes w) = w \otimes v .

5-

B = k [x_{1}, \dots, x_{t}] / I

6-

x_{1}, \dots, x_{t}

7-

i (J) = J .

8-

Δ := V \otimes_{k} B

9-

α : J \to Δ \otimes_{B} Δ^{'},

10-

Δ^{'} = B \otimes_{k} V

Formulas (html):

Correct Categorie: math

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1907.09832

Formulas:

1-

= \frac{1}{\sqrt{2}} (a + a^{†})

2-

= \frac{1}{i \sqrt{2}} (a - a^{†}),

3-

{| 0 ⟩, | 1 ⟩}

4-

{| q ⟩}_{q \in ℝ}

5-

⟨ k | ℓ ⟩ = δ_{k ℓ}

6-

k, ℓ \in {0, 1}

7-

⟨ q | q^{'} ⟩ = δ (q - q^{'})

8-

q, q^{'} \in ℝ

9-

| ψ ⟩ = ψ_{0} | 0 ⟩ + ψ_{1} | 1 ⟩

10-

| ψ ⟩ = \int 𝑑 q ψ (q) | q ⟩

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0506149

Formulas:

1-

P 4 m m

2-

c_{μ ν} \equiv \frac{\partial σ_{μ}}{\partial η_{ν}}

3-

C_{μ ν} = \frac{\partial^{2} E}{\partial η_{μ} \partial η_{ν}}

4-

c_{i j k l} = C_{i j k l} - δ_{i j} σ_{k l}

5-

d_{i ν} = \sum_{μ = 1}^{6} e_{i μ} s_{μ ν}

6-

P m \bar{3} m

7-

P 4 m m

8-

H = E + P V

9-

c_{11} = c_{22} = c_{33}

10-

c_{12} = c_{13} = c_{23}

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1811.05518

Formulas:

1-

K e p l e r

2-

K e p l e r

3-

σ_{B V S}

4-

u b v y

5-

B V g r i

6-

J H K_{S}

7-

T_{eff} = 6800 \pm 100

8-

\log g = 4.0 \pm 0.25

9-

[Fe / H] = 0.00 \pm 0.25

10-

A_{V} = 0.09 \pm 0.02

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/0406424

Formulas:

1-

r - D D O

2-

l o g (L / L_{☉}) \sim - 4.2

3-

8 k \times 8 k

4-

r - D D O = - 0.1

5-

r - D D O = - 0.75

6-

- 0.10 \geq r - D D O \geq - 0.45

7-

0.05 \leq r - z \leq 0.35

8-

- 0.45 \geq r - D D O \geq - 0.80

9-

0.35 \leq r - z \leq 0.65

10-

r - D D O 51

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1409.2946

Formulas:

1-

\dot{M} = 0.1 \times 10^{- 8} M_{⊙} {yr}^{- 1}

2-

\dot{M} = 2 \times 10^{- 8} M_{⊙} {yr}^{- 1}

3-

R \propto M^{0.226 - 0.262}

4-

Σ_{g} = \frac{\dot{M}}{3 π α (a) c_{s} h} \exp (\frac{- t}{τ_{dep}}) η,

5-

\dot{M} ≃ 2.5 \times 10^{- 8} {(\frac{M_{*}}{M_{⊙}})}^{1.3 \pm 0.3} M_{⊙} {yr}^{- 1} .

6-

\sim 2.5 \times 10^{- 8}

7-

M_{⊙} {yr}^{- 1}

8-

M_{⊙} {yr}^{- 1}

9-

α_{eff} (a) = \frac{α_{dead} - α_{mri}}{2} [\erf (\frac{a - a_{crit}}{0.1 a_{crit}}) + 1] + α_{mri},

10-

η = 0.5 [\erf (\frac{a - a_{mstr}}{0.1 a_{mstr}}) + 1],

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0912.5293

Formulas:

1-

| ψ (0) ⟩

2-

{| ⟨ ψ (0) | ψ (T_{rev}) ⟩ |}^{2}

3-

H = ℏ (χ a^{†} {}^{2}a^{2} + χ^{'} a^{†} {}^{3}a^{3}),

4-

[a, a^{†}] = 1

5-

a^{†} {}^{2}a^{2} = a^{†} a (a^{†} a - 1)

6-

a^{†} {}^{3}a^{3} = a^{†} a (a^{†} a - 1) (a^{†} a - 2)

7-

t = π / (k χ)

8-

U (t) = \exp (- i H t / ℏ)

9-

\exp [- i π n (n - 1) / k]

10-

U (π / k χ)

Formulas (html):

Correct Categorie: quant-ph

Guessed Categorie: quant-ph

Result: correct

Paper: https://arxiv.org/abs/cond-mat/0503516

Formulas:

1-

ϕ_{i} (𝐫)

2-

\frac{⟨ ψ | H | ψ ⟩}{⟨ ψ | ψ ⟩} .

3-

- \int ϕ_{i}^{*} (𝐫) Δ ϕ_{j} (𝐫) d 𝐫

4-

\int {(\nabla ϕ_{i} (𝐫))}^{*} \cdot \nabla ϕ_{j} (𝐫) d 𝐫 .

5-

⟨ H ϕ | ψ ⟩ = ⟨ ϕ | H ψ ⟩

6-

⟨ H ϕ | ψ ⟩ = ⟨ ϕ | H ψ ⟩

7-

H | ϕ ⟩ \in ℋ

8-

ϕ \in D (H)

9-

L^{2} (ℝ^{3})

10-

L^{2} (ℝ^{3})

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1012.5729

Formulas:

1-

ℑ m (- 1 / ϵ (q, ω))

2-

ℏ ω_{e x} = E_{n^{c}} (k + q) - E_{n^{v}} (k)

3-

△ n = n^{v} - n^{c}

4-

n^{c, v} = 0

5-

ω_{0} = v_{F} q

6-

1 / \sqrt{ω - ω_{0}}

7-

1 / \sqrt{ω_{0} - ω}

8-

υ_{q} {| ⟨ n; k + q | e^{i q y} | m; k ⟩ |}^{2}

9-

10^{5} / c m

10-

ℑ m [- 1 / ϵ (q, ω)]

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1907.11538

Formulas:

1-

α_{M L T}

2-

α_{M L T}

3-

α_{M L T}

4-

D_{o v} = D_{o} e x p (\frac{- 2 z}{H_{ν}})

5-

\frac{a d η_{j}}{d a} + \frac{6 ρ (a)}{\bar{ρ} (a)} (η_{j} + 1) + η_{j} (η_{j} - 1) = j (j + 1), j = 2, 3, 4

6-

η \equiv \frac{a}{ϵ_{j}} \frac{d ϵ_{j}}{d a},

7-

\bar{ρ} (a)

8-

k_{j} = \frac{j + 1 - η_{j} (R)}{2 (j + η_{j} (R))}

9-

Δ \log k_{2} \equiv \log k_{2, s t a n} - λ

10-

λ = 2 V^{2} / (3 g R)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0910.0193

Formulas:

1-

p p \to H \to W W \to e ν μ ν

2-

135 < m_{H} < 190

3-

160 < m_{H} < 170

4-

g g \to H \to W W

5-

q q / q g \to W W

6-

g g \to W W

7-

p p \to t \bar{t}

8-

H \to W W \to ℓ ν ℓ ν

9-

E_{T}^{m i s s} > 30

10-

| M_{τ τ} - M_{Z} | < 25

Formulas (html):

Correct Categorie: hep-ex

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/gr-qc/0404025

Formulas:

1-

f_{s} = 2 f_{r}

2-

s (t) = \frac{1}{2} F_{+} (t; ψ) h_{0} (1 + \cos^{2} ι) \cos Ψ (t) + F_{\times} (t; ψ) h_{0} \cos ι \sin Ψ (t),

3-

Ψ (t) = ϕ_{0} + 2 π [f_{s} (T - T_{0}) + \frac{1}{2} \dot{f_{s}} {(T - T_{0})}^{2}],

4-

T = t + δ t = t + \frac{\vec{r} \cdot \vec{n}}{c} + Δ T .

5-

\exp [- i Ψ (t)]

6-

y (t_{k}; 𝒂) = \frac{1}{4} F_{+} (t_{k}; ψ) h_{0} (1 + \cos^{2} ι) e^{i Δ Ψ (t)} - \frac{i}{2} F_{\times} (t_{k}; ψ) h_{0} \cos ι e^{i Δ Ψ (t)},

7-

𝒂 = (h_{0}, ψ, ϕ_{0}, \cos ι, Δ f, Δ \dot{f})

8-

Δ Ψ (t)

9-

ϕ_{0} + 2 π [Δ f (T - T_{0}) + Δ \dot{f} {(T - T_{0})}^{2} / 2]

10-

B_{k} = y (t_{k}; 𝒂) + ϵ_{k},

Formulas (html):

Correct Categorie: gr-qc

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0910.2448

Formulas:

1-

\tilde{g} \to \tilde{b} b \to {\tilde{χ}}_{2}^{0} b b \to {\tilde{τ}}_{1} τ b b \to {\tilde{χ}}_{1}^{0} τ τ b b

2-

8 f b^{- 1}

3-

\tilde{g} \to \tilde{b} b \to {\tilde{χ}}_{2}^{0} b b \to {\tilde{τ}}_{1} τ b b \to {\tilde{χ}}_{1}^{0} τ τ b b

4-

({\tilde{t}}_{L}, {\tilde{t}}_{R}), ({\tilde{b}}_{L}, {\tilde{b}}_{R})

5-

({\tilde{τ}}_{L}, {\tilde{τ}}_{R})

6-

100 - 300 {fb}^{- 1}

7-

t a n β

8-

m_{{\tilde{t a u}}_{1}}

9-

\tilde{g} \overset{16.6 %}{⟶} {\tilde{b}}_{1} \overset{24.1 %}{⟶} {\tilde{χ}}_{2}^{0} \overset{48.7 %}{⟶} {\tilde{τ}}_{1} \overset{100 %}{⟶} {\tilde{χ}}_{1}^{0} \Rightarrow 1.96 %

10-

\tilde{g} \overset{9.2 %}{⟶} {\tilde{b}}_{2} \overset{16.6 %}{⟶} {\tilde{χ}}_{2}^{0} \overset{48.7 %}{⟶} {\tilde{τ}}_{1} \overset{100 %}{⟶} {\tilde{χ}}_{1}^{0} \Rightarrow 0.75 %

Formulas (html):

Correct Categorie: hep-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/0901.1982

Formulas:

1-

\sim (1 - 3) \times 10^{5} r_{g}

2-

(4 - 7) r_{g}

3-

10^{4 - 5} r_{g}

4-

r_{g} \equiv G M / c^{2}

5-

H R 2 < 1.1

6-

H R 2 = 1.1

7-

f = 1 - \exp (- 7.5 R)

8-

1 / (1 - f) ≃ 1 + 7.5 R

9-

N_{H} = 3 \times 10^{21}

10-

Q = ν_{0} / FWHM \approx 11

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1003.3856

Formulas:

1-

τ_{26} = 1.03 \times 10^{6}

2-

{}^{27}{Al} = 5 \times 10^{- 5}

3-

R_{SB} ≃ (22 pc) t_{Myr}^{3 / 5} N_{*, 30}^{1 / 5} n_{H, 100}^{- 1 / 5},

4-

N_{*, 30} = N_{*} / 30

5-

n_{H, 100} = n_{H} / (100 {cm}^{- 3})

6-

(5.7 \times 10^{6} K) t_{Myr}^{- 6 / 35} N_{*, 30}^{8 / 35} n_{H, 100}^{2 / 35},

7-

(0.17 {cm}^{- 3}) t_{Myr}^{- 22 / 35} N_{*, 30}^{6 / 35} n_{H, 100}^{19 / 35} .

8-

Δ E_{γ} = 1

9-

v_{\max} \sim 0.5 c Δ E_{γ} / E_{γ} \sim 150

10-

X_{gr} = a_{gr} ρ_{gr} = (2 \times 10^{- 6} g {cm}^{- 2}) (a_{gr} / 0.01 μ m)

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/1701.03108

Formulas:

1-

D \bar{\nabla} \hat{g} \bar{\nabla} \hat{g} + i [ε {\hat{ρ}}_{3} + \hat{𝝈} \cdot 𝒉, \hat{g}] = 0

2-

{\hat{ρ}}_{3} = diag (+ 1, + 1, - 1, - 1)

3-

\hat{𝝈} = diag (𝝈, 𝝈^{*})

4-

\hat{g} = \hat{g} (x, y, ε)

5-

\hat{g} = (\begin{matrix} g & f \\ - \tilde{f} & - \tilde{g} \end{matrix})

6-

ε \to (- ε)

7-

\bar{\nabla} \hat{g} = \nabla \hat{g} - i [\hat{𝑨}, \hat{g}]

8-

\hat{𝑨} = diag (𝑨, - 𝑨^{*})

9-

𝑨 = - α (σ_{y} 𝒆_{𝒙} - σ_{x} 𝒆_{𝒚})

10-

𝒆_{N} \cdot \bar{\nabla} \hat{g} = \frac{1}{ζ L} [{\hat{g}}_{R}, {\hat{g}}_{L}]

Formulas (html):

Correct Categorie: cond-mat

Guessed Categorie: quant-ph

Result: incorrect

Paper: https://arxiv.org/abs/astro-ph/9901271

Formulas:

1-

M / L_{B} \sim 13 h

2-

68 ″ \times 81 ″

3-

0 \overset{''}{.} 045

4-

0 \overset{''}{.} 09

5-

0 \overset{''}{.} 286

6-

0 \overset{''}{.} 7

7-

0 \overset{''}{.} 18

8-

0 \overset{''}{.} 18

9-

ω (z, \bar{z}) = z - \nabla Φ (z, \bar{z}),

10-

\nabla = 2 \partial / \partial \bar{z}

Formulas (html):

Correct Categorie: astro-ph

Guessed Categorie: quant-ph

Result: incorrect

Run 11332251 (Agent494)