# Integral

Submitted by schubotz on

# Results for NTCIR10-FS-19

## Query

### Original Query

### Compiled by FSE

#### Token-Filter

- TeXFilter:
`[f, mathbf x 2, d, Rf, int, L x 2, ( x 2, ) x 2, ,, \ x 4, _, | x 2, =, x x 2]`

- Presentation-MathML:
`[f x 2, d, R, L x 2, ? x 2, | x 2, =, ∫]`

#### MathML-Filter

#### Word filter

No words found specifified. Rendered Presentation-MathML:## Results

### Summary

#### Reviewer score 2

- Items reviewd: 24
- Accumulated score: 1080983
- Formulasearchengine found: 4

#### Reviewer score 0

- Items reviewd: 76
- Accumulated score: 3780713
- Formulasearchengine found: 14

++ | + | o | ∑ | |
---|---|---|---|---|

200000+ | 0 | 4 | 14 | 18 |

5000-200000 | 0 | 0 | 0 | 0 |

<5000 | 0 | 20 | 62 | 82 |

∑ | 0 | 24 | 76 | 100 |

### Short result list

### Detailed results for reviewer score 2

#### Hit idp1309600

- Reviwer: xxx
- Reviwer score: 2
- Formulasearchengine rank: 1
- Formulasearchengine score: 270554
- Reference to collection: _PREFIX_/205/f081892.xhtml#idp1309600

Rendered MathML:

$\displaystyle Q(f_{{R,\Delta R}},g_{{T}})=\int j_{{0}}(\mathbf{x},t)f_{{R,\Delta R}}(\mathbf{x})g_{{T}}(t)d\mathbf{x}dt,~{}lim_{{R\rightarrow\infty}}Q(f_{{R,\Delta R}},g_{{T}})=Q$

End of MathML

.

#### Hit id87198

- Reviwer: xxx
- Reviwer score: 2
- Formulasearchengine rank: 2
- Formulasearchengine score: 270398
- Reference to collection: _PREFIX_/29/f011229.xhtml#id87198

Rendered MathML:

End of MathML

.

#### Hit id56051

- Reviwer: xxx
- Reviwer score: 2
- Formulasearchengine rank: 8
- Formulasearchengine score: 270086
- Reference to collection: _PREFIX_/147/f058567.xhtml#id56051

Rendered MathML:

End of MathML

.

#### Hit id55428

- Reviwer: xxx
- Reviwer score: 2
- Formulasearchengine rank: 15
- Formulasearchengine score: 269945
- Reference to collection: _PREFIX_/185/f073828.xhtml#id55428

Rendered MathML:

End of MathML

.

#### Hit id64398

- Reviwer: xxx
- Reviwer score: 2
- Formulasearchengine rank: 19
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/101/f040014.xhtml#id64398

Rendered MathML:

End of MathML

.

#### Hit id87433

- Reviwer: xxx
- Reviwer score: 2
- Formulasearchengine rank: 20
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/217/f086773.xhtml#id87433

Rendered MathML:

End of MathML

.

#### Hit idp1349520

- Reviwer: xxx
- Reviwer score: 2
- Formulasearchengine rank: 21
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/204/f081465.xhtml#idp1349520

Rendered MathML:

$J({\bf x})=q\int d^{2}x^{{\prime}}\rho({\bf x}^{{\prime}})log(z-z^{{\prime}})-\frac{|z|^{2}}{4l^{2}}$

End of MathML

.

#### Hit idp14766608

- Reviwer: xxx
- Reviwer score: 2
- Formulasearchengine rank: 22
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/129/f051455.xhtml#idp14766608

Rendered MathML:

$\varepsilon _{{I}}=\frac{1}{2V}\int d\mathbf{x}_{{1}}d\mathbf{x}_{{2}}\rho(\mathbf{x}_{{1}})\frac{g^{{2}}}{4\pi}\frac{e^{{-\mu r}}}{r}\rho(\mathbf{x}_{{2}}),$

End of MathML

.

#### Hit idp20563520

- Reviwer: xxx
- Reviwer score: 2
- Formulasearchengine rank: 23
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/129/f051419.xhtml#idp20563520

Rendered MathML:

$\displaystyle\nabla\cdot\int _{{t_{{0}}}}^{{t}}\mathbf{J}(\mathbf{x},t^{{\prime}})\,{\rm d}t^{{\prime}}=-\rho(\mathbf{x},t).$

End of MathML

.

#### Hit idp20710704

- Reviwer: xxx
- Reviwer score: 2
- Formulasearchengine rank: 24
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/129/f051419.xhtml#idp20710704

Rendered MathML:

$\displaystyle\begin{split}\hat{\mathbf{E}}(\mathbf{x},s)&=\int _{{\mathbf{x}^{{\prime}}\in{\mathbb{R}}^{{3}}}}\frac{e^{{-(s/c)|\mathbf{x}-\mathbf{x}^{{\prime}}|}}}{4\pi|\mathbf{x}-\mathbf{x}^{{\prime}}|^{{3}}}\left[3{\mathbb{Q}}-{\mathbb{I}}\right]\frac{1}{s\varepsilon _{{0}}}\hat{\mathbf{J}}(\mathbf{x}^{{\prime}},s)\,{\rm d}\mathbf{x}^{{\prime}}\\ &+\int _{{\mathbf{x}^{{\prime}}\in{\mathbb{R}}^{{3}}}}\frac{e^{{-(s/c)|\mathbf{x}-\mathbf{x}^{{\prime}}|}}}{4\pi|\mathbf{x}-\mathbf{x}^{{\prime}}|^{{2}}}\left[3{\mathbb{Q}}-{\mathbb{I}}\right]\frac{1}{\varepsilon _{{0}}c}\hat{\mathbf{J}}(\mathbf{x}^{{\prime}},s)\,{\rm d}\mathbf{x}^{{\prime}}\\ &+\int _{{\mathbf{x}^{{\prime}}\in{\mathbb{R}}^{{3}}}}\frac{e^{{-(s/c)|\mathbf{x}-\mathbf{x}^{{\prime}}|}}}{4\pi|\mathbf{x}-\mathbf{x}^{{\prime}}|}\left[{\mathbb{Q}}-{\mathbb{I}}\right]\frac{s}{\varepsilon _{{0}}c^{{2}}}\hat{\mathbf{J}}(\mathbf{x}^{{\prime}},s)\,{\rm d}\mathbf{x}^{{\prime}}.\end{split}$

End of MathML

.

#### Hit idp20929088

- Reviwer: xxx
- Reviwer score: 2
- Formulasearchengine rank: 25
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/129/f051419.xhtml#idp20929088

Rendered MathML:

$\displaystyle\begin{split}\hat{\mathbf{H}}(\mathbf{x},s)&=-\int _{{\mathbf{x}^{{\prime}}\in{\mathbb{R}}^{{3}}}}\frac{e^{{-(s/c)|\mathbf{x}-\mathbf{x}^{{\prime}}|}}}{4\pi|\mathbf{x}-\mathbf{x}^{{\prime}}|^{{2}}}\mathbf{\Theta}\times\hat{\mathbf{J}}(\mathbf{x}^{{\prime}},s)\,{\rm d}\mathbf{x}^{{\prime}}\\ &-\int _{{\mathbf{x}^{{\prime}}\in{\mathbb{R}}^{{3}}}}\frac{e^{{-(s/c)|\mathbf{x}-\mathbf{x}^{{\prime}}|}}}{4\pi|\mathbf{x}-\mathbf{x}^{{\prime}}|}\frac{s}{c}\mathbf{\Theta}\times\hat{\mathbf{J}}(\mathbf{x}^{{\prime}},s)\,{\rm d}\mathbf{x}^{{\prime}},\end{split}$

End of MathML

.

#### Hit idp25958672

- Reviwer: xxx
- Reviwer score: 2
- Formulasearchengine rank: 26
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/62/f024626.xhtml#idp25958672

Rendered MathML:

$\widehat{\rm Val}({\cal G})=\sigma _{{\cal G}}U^{N}\sum _{{\rho _{1},\ldots,\rho _{N}}}\int d{\bf x}_{1}\cdots d{\bf x}_{N}\prod _{{\ell\in{\cal G}}}\delta _{{\sigma(\ell),\sigma^{{\prime}}(\ell)}}g_{{\rho(\ell),\rho^{{\prime}}(\ell)}}({\bf x}(\ell)-{\bf x}^{{\prime}}(\ell))\;,$

End of MathML

.

#### Hit idp28232816

- Reviwer: xxx
- Reviwer score: 2
- Formulasearchengine rank: 27
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/114/f045579.xhtml#idp28232816

Rendered MathML:

$P(\mathbf{y})=\int d\mathbf{x}P(\mathbf{x})\delta _{D}\left(\mathbf{y}-\mathbf{F}(\mathbf{x})\right)\;,$

End of MathML

.

#### Hit idp482592

- Reviwer: xxx
- Reviwer score: 2
- Formulasearchengine rank: 28
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/85/f033618.xhtml#idp482592

Rendered MathML:

$Z_{{QCD(R)}}\left(\beta,\mu\right)=\int{\mathrm{\cal D}}A\, e^{{-S_{{YM}}(A)}}\int{\mathrm{\cal D}}{\bar{\psi}}{\mathrm{\cal D}}\psi e^{{-\int _{0}^{{\beta}}{\mathrm{d}}\tau\int{\mathrm{d}}^{3}{\bf x}\,{\bar{\psi}}\left({\hbox{\kern 2.25pt/}{D}}_{R}-\gamma _{0}{\cal M}+M\right)\psi}},$

End of MathML

.

#### Hit idp524848

- Reviwer: xxx
- Reviwer score: 2
- Formulasearchengine rank: 29
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/129/f051419.xhtml#idp524848

Rendered MathML:

$\displaystyle\nabla\cdot\mathbf{E}(\mathbf{x},t)=-\frac{1}{\varepsilon _{{0}}}\nabla\cdot\int _{{t_{{0}}}}^{{t}}\mathbf{J}(\mathbf{x},t^{{\prime}})\,{\rm d}t^{{\prime}}.$

End of MathML

.

#### Hit idp6530160

- Reviwer: xxx
- Reviwer score: 2
- Formulasearchengine rank: 30
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/85/f033618.xhtml#idp6530160

Rendered MathML:

$Z_{{QCD(R)}}\left(\beta,\mu\right)=\int{\mathrm{\cal D}}A\, e^{{-S_{{YM}}(A)}}\int{\mathrm{\cal D}}{\bar{\psi}}{\mathrm{\cal D}}\psi e^{{-\int _{0}^{{\beta}}{\mathrm{d}}\tau\int{\mathrm{d}}^{3}{\bf x}\,{\bar{\psi}}\left({\hbox{\kern 2.25pt/}{D}}_{R}-\gamma _{0}{\cal M}+M\right)\psi}},$

End of MathML

.

#### Hit idp667024

- Reviwer: xxx
- Reviwer score: 2
- Formulasearchengine rank: 31
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/130/f051918.xhtml#idp667024

Rendered MathML:

$m_{i}=\int _{{{\bf X}_{i}-{\bf h}_{i}}}^{{{\bf X}_{i}+{\bf h}_{i}}}\sum _{{j=1}}^{{N}}C_{j}({\bf x})\ {\rm d}^{D}{\bf x}$

End of MathML

.

#### Hit idp6981680

- Reviwer: xxx
- Reviwer score: 2
- Formulasearchengine rank: 32
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/213/f085146.xhtml#idp6981680

Rendered MathML:

$\int|\mathbf{V}(\mathbf{x}_{1},\ldots,\mathbf{x}_{m})|\prod _{{j=1}}^{m}\chi _{{\mathbf{E}_{j}}}(\mathbf{x}_{j})d\mathbf{x}_{1}\cdots d\mathbf{x}_{m}\geq c^{N}\prod _{{j=1}}^{m}|\mathbf{E}_{j}|^{\frac{1}{p_{j}}}$

End of MathML

.

#### Hit idp7168864

- Reviwer: xxx
- Reviwer score: 2
- Formulasearchengine rank: 33
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/213/f085146.xhtml#idp7168864

Rendered MathML:

$\begin{split}\int|\mathbf{V}(\mathbf{x}_{1},\ldots,\mathbf{x}_{m})|&\prod _{{j=1}}^{m}\chi _{{\mathbf{E}_{j}}}(\mathbf{x}_{j})dx_{1}^{1}\cdots dx_{m}^{1}\\ &\geq c\prod _{{i=2}}^{N}|V(x_{1}^{i},\ldots,x_{m}^{i})|\prod _{{j=1}}^{m}\left(\int\left(\chi _{{\mathbf{E}_{j}}}(\mathbf{x}_{j})\right)^{{p_{j}}}dx_{j}^{1}\right)^{\frac{1}{p_{j}}}.\end{split}$

End of MathML

.

#### Hit idp799472

- Reviwer: xxx
- Reviwer score: 2
- Formulasearchengine rank: 34
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/129/f051419.xhtml#idp799472

Rendered MathML:

$\displaystyle\mathbf{E}(\mathbf{x},t)=c^{{2}}\nabla\nabla\cdot\int _{{t_{{0}}}}^{{t}}\mathbf{A}(\mathbf{x},t^{{\prime}})\,{\rm d}t^{{\prime}}-\partial _{{t}}\mathbf{A}(\mathbf{x},t).$

End of MathML

.

#### Hit idp8398064

- Reviwer: xxx
- Reviwer score: 2
- Formulasearchengine rank: 35
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/213/f085146.xhtml#idp8398064

Rendered MathML:

$\int\chi _{{\mathbf{\Omega}}}(\varphi _{r}^{{\mathbf{x}}}(\mathbf{t},\mathbf{u}))d\mathbf{x}=\chi _{{\mathbf{F}}}(\pi _{{{\mathcal{A}}}}(\mathbf{t},\mathbf{u}))\int\chi _{{\mathbf{G}}}(\widehat{\varphi}^{{\mathbf{x}}}_{r}(\mathbf{t},\mathbf{u}))d\mathbf{x}.$

End of MathML

.

#### Hit idp890688

- Reviwer: xxx
- Reviwer score: 2
- Formulasearchengine rank: 36
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/129/f051419.xhtml#idp890688

Rendered MathML:

$\displaystyle c^{2}\nabla\cdot\int _{{t_{{0}}}}^{{t}}\mathbf{A}(\mathbf{x},t^{{\prime}})\,{\rm d}t^{{\prime}}=-\phi(\mathbf{x},t).$

End of MathML

.

#### Hit idp9447072

- Reviwer: xxx
- Reviwer score: 2
- Formulasearchengine rank: 37
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/85/f033618.xhtml#idp9447072

Rendered MathML:

$\displaystyle=\int{\cal D}A{\cal D}C{\cal D}{\bar{C}}\int{\cal D}\psi{\cal D}{\bar{\psi}}e^{{-\int _{0}^{{\beta}}{\mathrm{d}}\tau\int{\mathrm{d}}^{3}{\bf x}{\cal L}_{{QCD(R)}}}}$

End of MathML

.

#### Hit idp9941376

- Reviwer: xxx
- Reviwer score: 2
- Formulasearchengine rank: 38
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/176/f070398.xhtml#idp9941376

Rendered MathML:

$\int d{\bf x}\; F({\bf x})=1$

End of MathML

.

### Detailed results for reviewer score 0

#### Hit idp45725680

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 3
- Formulasearchengine score: 270301
- Reference to collection: _PREFIX_/62/f024626.xhtml#idp45725680

Rendered MathML:

${\cal D}^{*}({\rm d}\psi)=\prod _{{\substack{f\in P\\ f\not\in T}}}d\psi^{{\varepsilon(f)}}_{{{\bf x}(f),\sigma(f),\rho(f)}}\;,\qquad V^{*}({\bf t})=\sum _{{\ell\in L(X)}}t_{{n^{{\prime}}(\ell)}}\ldots t_{{n(\ell)}}\, V^{T}_{{\ell}}$

End of MathML

.

#### Hit idp27943520

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 4
- Formulasearchengine score: 270271
- Reference to collection: _PREFIX_/114/f045579.xhtml#idp27943520

Rendered MathML:

$\Phi(\mathbf{x})=\Phi _{L}(\mathbf{x})+f_{{\rm NL}}^{{\rm loc.}}\left[\Phi^{2}_{L}(\mathbf{x})-\left\langle\Phi^{2}_{L}(\mathbf{x})\right\rangle\right]\;.$

End of MathML

.

#### Hit idp35501728

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 5
- Formulasearchengine score: 270271
- Reference to collection: _PREFIX_/114/f045579.xhtml#idp35501728

Rendered MathML:

$\Phi(\mathbf{x})=\Phi _{L}(\mathbf{x})+f_{\textrm{NL}}\left[\Phi _{L}^{2}(\mathbf{x})-\left\langle\Phi _{L}^{2}(\mathbf{x})\right\rangle\right]\;.$

End of MathML

.

#### Hit idp36464384

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 6
- Formulasearchengine score: 270191
- Reference to collection: _PREFIX_/62/f024626.xhtml#idp36464384

Rendered MathML:

$\int P_{{f_{h},\overline{A}_{{h-1}}}}(d\psi^{{(h)}})\psi^{{(h)-}}_{{{\bf x}_{1},\sigma _{1},\omega _{1}}}\psi^{{(h)+}}_{{{\bf x}_{2},\sigma _{2},\omega _{2}}}=\delta _{{\sigma _{1},\sigma _{2}}}\delta _{{\omega _{1},\omega _{2}}}g^{{(h)}}_{\omega}({\bf x}_{1}-{\bf x}_{2})\;,$

End of MathML

.

#### Hit idp45014352

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 7
- Formulasearchengine score: 270188
- Reference to collection: _PREFIX_/62/f024626.xhtml#idp45014352

Rendered MathML:

${\cal D}\psi _{{Y^{i}}}=\prod _{{j\in Y^{i}}}\Big[\prod _{{f\in P_{{j}}^{+}}}{\rm d}\psi^{{+}}_{{{\bf x}(f),\sigma(f),\rho(f)}}\Big]\Big[\prod _{{f\in P_{{j}}^{-}}}{\rm d}\psi^{{-}}_{{{\bf x}(f),\sigma(f),\rho(f)}}\Big]$

End of MathML

.

#### Hit idp890800

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 9
- Formulasearchengine score: 270050
- Reference to collection: _PREFIX_/114/f045579.xhtml#idp890800

Rendered MathML:

$\displaystyle\Phi _{{\rm L}}({\bf x})+f_{\textrm{NL}}\big[\Phi^{2}_{{\rm L}}({\bf x})-\langle\Phi^{2}_{{\rm L}}({\bf x})\rangle\big]\,,$

End of MathML

.

#### Hit id59054

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 10
- Formulasearchengine score: 269996
- Reference to collection: _PREFIX_/33/f013176.xhtml#id59054

Rendered MathML:

End of MathML

.

#### Hit idp808832

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 11
- Formulasearchengine score: 269993
- Reference to collection: _PREFIX_/130/f051918.xhtml#idp808832

Rendered MathML:

$\hat{f}_{{\rm B}}({\bf x})=\frac{1}{\prod _{{d=1}}^{{D}}2\hat{h}_{{Kd}}({\bf x})}\int _{{{\bf x}-\hat{\bf h}_{K}({\bf x})}}^{{{\bf x}+\hat{\bf h}_{K}({\bf x})}}\hat{f}_{K}({\bf x}_{0})\ {\rm d}^{D}{\bf x}_{0}$

End of MathML

.

#### Hit idp28430608

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 12
- Formulasearchengine score: 269959
- Reference to collection: _PREFIX_/114/f045579.xhtml#idp28430608

Rendered MathML:

${\cal{O}}\left(f_{\textrm{NL}}\left\langle\Phi _{L}(\mathbf{x})\right\rangle\right)$

End of MathML

.

#### Hit idp29649600

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 13
- Formulasearchengine score: 269959
- Reference to collection: _PREFIX_/114/f045579.xhtml#idp29649600

Rendered MathML:

${\cal{O}}\left(f_{\textrm{NL}}\left\langle\Phi^{2}_{L}(\mathbf{x})\right\rangle\right)$

End of MathML

.

#### Hit idp35232736

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 14
- Formulasearchengine score: 269959
- Reference to collection: _PREFIX_/114/f045579.xhtml#idp35232736

Rendered MathML:

${\cal{O}}\left(f_{\textrm{NL}}\left\langle\Phi^{2}_{L}(\mathbf{x})\right\rangle\right)$

End of MathML

.

#### Hit id59970

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 16
- Formulasearchengine score: 269933
- Reference to collection: _PREFIX_/29/f011229.xhtml#id59970

Rendered MathML:

End of MathML

.

#### Hit id71027

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 17
- Formulasearchengine score: 269882
- Reference to collection: _PREFIX_/36/f014324.xhtml#id71027

Rendered MathML:

End of MathML

.

#### Hit id59033

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 18
- Formulasearchengine score: 269760
- Reference to collection: _PREFIX_/146/f058265.xhtml#id59033

Rendered MathML:

End of MathML

.

#### Hit id123799

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 39
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/243/f097132.xhtml#id123799

Rendered MathML:

End of MathML

.

#### Hit id128218

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 40
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/31/f012303.xhtml#id128218

Rendered MathML:

End of MathML

.

#### Hit id134299

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 41
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/162/f064427.xhtml#id134299

Rendered MathML:

End of MathML

.

#### Hit id53596

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 42
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/241/f096312.xhtml#id53596

Rendered MathML:

End of MathML

.

#### Hit id53793

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 43
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/125/f049766.xhtml#id53793

Rendered MathML:

End of MathML

.

#### Hit id54181

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 44
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/30/f011890.xhtml#id54181

Rendered MathML:

End of MathML

.

#### Hit id54293

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 45
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/32/f012785.xhtml#id54293

Rendered MathML:

End of MathML

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#### Hit id54410

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 46
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/39/f015432.xhtml#id54410

Rendered MathML:

End of MathML

.

#### Hit id55205

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 47
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/106/f042100.xhtml#id55205

Rendered MathML:

End of MathML

.

#### Hit id55238

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 48
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/94/f037263.xhtml#id55238

Rendered MathML:

End of MathML

.

#### Hit id55249

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 49
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/142/f056597.xhtml#id55249

Rendered MathML:

End of MathML

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#### Hit id55284

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 50
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/79/f031397.xhtml#id55284

Rendered MathML:

End of MathML

.

#### Hit id55524

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 51
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/229/f091235.xhtml#id55524

Rendered MathML:

End of MathML

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#### Hit id55857

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 52
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/95/f037849.xhtml#id55857

Rendered MathML:

End of MathML

.

#### Hit id56729

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 53
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/197/f078423.xhtml#id56729

Rendered MathML:

End of MathML

.

#### Hit id57005

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 54
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/200/f079781.xhtml#id57005

Rendered MathML:

End of MathML

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#### Hit id57128

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 55
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/234/f093508.xhtml#id57128

Rendered MathML:

End of MathML

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#### Hit id57270

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 56
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/181/f072289.xhtml#id57270

Rendered MathML:

End of MathML

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#### Hit id57718

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 57
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/98/f039060.xhtml#id57718

Rendered MathML:

End of MathML

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#### Hit id59046

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 58
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/146/f058358.xhtml#id59046

Rendered MathML:

End of MathML

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#### Hit id59103

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 59
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/6/f002375.xhtml#id59103

Rendered MathML:

End of MathML

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#### Hit id59668

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 60
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/173/f068817.xhtml#id59668

Rendered MathML:

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#### Hit id61000

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 61
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/27/f010506.xhtml#id61000

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#### Hit id61288

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 62
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/176/f070179.xhtml#id61288

Rendered MathML:

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#### Hit id61586

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 63
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/65/f025635.xhtml#id61586

Rendered MathML:

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#### Hit id62105

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 64
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/208/f082869.xhtml#id62105

Rendered MathML:

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#### Hit id62832

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 65
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/96/f038212.xhtml#id62832

Rendered MathML:

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#### Hit id63307

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 66
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/43/f017045.xhtml#id63307

Rendered MathML:

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#### Hit id63411

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 67
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/191/f076180.xhtml#id63411

Rendered MathML:

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#### Hit id63575

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 68
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/109/f043399.xhtml#id63575

Rendered MathML:

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#### Hit id63782

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 69
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/53/f021075.xhtml#id63782

Rendered MathML:

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#### Hit id64087

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 70
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/182/f072548.xhtml#id64087

Rendered MathML:

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#### Hit id65514

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 71
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/162/f064570.xhtml#id65514

Rendered MathML:

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#### Hit id68355

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 72
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/82/f032700.xhtml#id68355

Rendered MathML:

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#### Hit id73406

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 73
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/168/f067128.xhtml#id73406

Rendered MathML:

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#### Hit id74460

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 74
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/32/f012585.xhtml#id74460

Rendered MathML:

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#### Hit id75382

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 75
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/21/f008176.xhtml#id75382

Rendered MathML:

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#### Hit id75554

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 76
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/72/f028518.xhtml#id75554

Rendered MathML:

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#### Hit id75678

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 77
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/227/f090742.xhtml#id75678

Rendered MathML:

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#### Hit id75984

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 78
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/93/f037108.xhtml#id75984

Rendered MathML:

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#### Hit id79621

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 79
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/208/f082850.xhtml#id79621

Rendered MathML:

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#### Hit id80666

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 80
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/250/f099718.xhtml#id80666

Rendered MathML:

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#### Hit id81032

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 81
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/199/f079571.xhtml#id81032

Rendered MathML:

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#### Hit id85947

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 82
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/96/f038229.xhtml#id85947

Rendered MathML:

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#### Hit id90998

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 83
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/120/f047612.xhtml#id90998

Rendered MathML:

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#### Hit id91005

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 84
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/20/f007960.xhtml#id91005

Rendered MathML:

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#### Hit id95964

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 85
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/127/f050483.xhtml#id95964

Rendered MathML:

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#### Hit id96512

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 86
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/226/f090309.xhtml#id96512

Rendered MathML:

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#### Hit id96766

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 87
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/184/f073597.xhtml#id96766

Rendered MathML:

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#### Hit idp20645904

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 88
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/129/f051419.xhtml#idp20645904

Rendered MathML:

$\displaystyle\hat{\mathbf{A}}(\mathbf{x},s)=\mu _{{0}}\int _{{\mathbf{x}^{{\prime}}\in{\mathbb{R}}^{{3}}}}g(\mathbf{x}-\mathbf{x}^{{\prime}},s)\hat{\mathbf{J}}(\mathbf{x}^{{\prime}},s)\,{\rm d}\mathbf{x}^{{\prime}},$

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#### Hit idp21036224

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 89
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/129/f051419.xhtml#idp21036224

Rendered MathML:

$\displaystyle\begin{split}\mathbf{E}(\mathbf{x},t)&=\int _{{\mathbf{x}^{{\prime}}\in{\mathbb{R}}^{{3}}}}\frac{3{\mathbb{Q}}-{\mathbb{I}}}{4\pi|\mathbf{x}-\mathbf{x}^{{\prime}}|^{{3}}}\frac{1}{\varepsilon _{{0}}}\int _{{t_{{0}}}}^{{t_{{\rm R}}}}\mathbf{J}(\mathbf{x}^{{\prime}},t^{{\prime}})\,{\rm d}t^{{\prime}}\,{\rm d}\mathbf{x}^{{\prime}}\\ &+\int _{{\mathbf{x}^{{\prime}}\in{\mathbb{R}}^{{3}}}}\frac{3{\mathbb{Q}}-{\mathbb{I}}}{4\pi|\mathbf{x}-\mathbf{x}^{{\prime}}|^{{2}}}\frac{1}{\varepsilon _{{0}}c}\mathbf{J}(\mathbf{x}^{{\prime}},t_{{\rm R}})\,{\rm d}\mathbf{x}^{{\prime}}\\ &+\int _{{\mathbf{x}^{{\prime}}\in{\mathbb{R}}^{{3}}}}\frac{{\mathbb{Q}}-{\mathbb{I}}}{4\pi|\mathbf{x}-\mathbf{x}^{{\prime}}|}\frac{1}{\varepsilon _{{0}}c^{{2}}}\partial _{{t}}\mathbf{J}(\mathbf{x}^{{\prime}},t_{{\rm R}})\,{\rm d}\mathbf{x}^{{\prime}}\end{split}$

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#### Hit idp21165680

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 90
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/129/f051419.xhtml#idp21165680

Rendered MathML:

$\displaystyle\begin{split}\mathbf{H}(\mathbf{x},t)&=-\int _{{\mathbf{x}^{{\prime}}\in{\mathbb{R}}^{{3}}}}\frac{1}{4\pi|\mathbf{x}-\mathbf{x}^{{\prime}}|^{{2}}}\mathbf{\Theta}\times\mathbf{J}(\mathbf{x}^{{\prime}},t_{{\rm R}})\,{\rm d}\mathbf{x}^{{\prime}}\\ &-\int _{{\mathbf{x}^{{\prime}}\in{\mathbb{R}}^{{3}}}}\frac{1}{4\pi|\mathbf{x}-\mathbf{x}^{{\prime}}|}\mathbf{\Theta}\times\frac{1}{c}\partial _{{t}}\mathbf{J}(\mathbf{x}^{{\prime}},t_{{\rm R}}),\,{\rm d}\mathbf{x}^{{\prime}}\end{split}$

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#### Hit idp21239920

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 91
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/129/f051419.xhtml#idp21239920

Rendered MathML:

$\displaystyle t_{{\rm R}}=t-\frac{|\mathbf{x}-\mathbf{x}^{{\prime}}|}{c},$

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#### Hit idp23899936

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 92
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/62/f024626.xhtml#idp23899936

Rendered MathML:

$V_{{\beta,\Lambda}}(\Psi):=U\sum _{{\rho=1,2}}\int _{{(\beta,\Lambda)}}d{\bf x}\big(\Psi _{{{\bf x},\uparrow,\rho}}^{+}\Psi _{{{\bf x},\uparrow,\rho}}^{-}-\frac{1}{2}\big)\big(\Psi _{{{\bf x},\downarrow,\rho}}^{+}\Psi _{{{\bf x},\downarrow,\rho}}^{-}-\frac{1}{2}\big)\;,$

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#### Hit idp24939008

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 93
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/62/f024626.xhtml#idp24939008

Rendered MathML:

${\cal V}(\psi)=U\sum _{{\rho=1,2}}\int _{{(\beta,\Lambda)}}d{\bf x}\,\psi^{+}_{{{\bf x},\uparrow,\rho}}\psi^{-}_{{{\bf x},\uparrow,\rho}}\psi^{+}_{{{\bf x},\downarrow,\rho}}\psi^{-}_{{{\bf x},\downarrow,\rho}}\;,$

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#### Hit idp38173968

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 94
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/114/f045579.xhtml#idp38173968

Rendered MathML:

$\delta _{R}({\bf x})=\int d^{3}x^{{\prime}}W_{R}({\bf x}-{\bf x}^{{\prime}})\delta({\bf x}^{{\prime}})$

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#### Hit idp38872272

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 95
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/62/f024626.xhtml#idp38872272

Rendered MathML:

$\int\prod _{{\ell\in T^{*}\setminus\cup _{v}T_{v}}}d({\bf x}(\ell)-{\bf x}^{{\prime}}(\ell))\prod _{{i=1}}^{n}|K_{{v_{i}^{*}}}^{{(h_{i})}}({\bf x}_{{v_{i}^{*}}})|\leq\prod _{{i=1}}^{n}C^{{p_{i}}}|U|^{{\,\frac{p_{i}}{2}-1}}\;,$

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#### Hit idp4041648

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 96
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/111/f044359.xhtml#idp4041648

Rendered MathML:

$R_{i}=\{{\mathbf{x}}\in L_{i}\>:\> Q({\mathbf{x}})=a\ \mathrm{and}\ {\mathbf{x}}\ \mathrm{is\ primitive\ in}\ L_{i}\}.$

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#### Hit idp574176

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 97
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/114/f045579.xhtml#idp574176

Rendered MathML:

$\displaystyle\Phi({\bf x},\, t)=\int\frac{d^{3}{\bf k}}{(2\pi)^{3}}\, e^{{-i{\bf k\cdot x}}}\,\Phi({\bf k},t)\,.$

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#### Hit idp6573776

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 98
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/111/f044359.xhtml#idp6573776

Rendered MathML:

$\{{{\mathbf{x}}}\in L\>:\> Q({{\mathbf{x}}})\equiv 0\;\;(\mathop{{\rm mod}}d)\}$

End of MathML

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#### Hit idp7030256

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 99
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/111/f044359.xhtml#idp7030256

Rendered MathML:

$\{{{\mathbf{x}}}\in L\setminus\{ 0\}\>:\> Q({{\mathbf{x}}})\equiv 0\;\;(\mathop{{\rm mod}}d)\}.$

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#### Hit idp9485696

- Reviwer: xxx
- Reviwer score: 0
- Formulasearchengine rank: 100
- Formulasearchengine score: 0
- Reference to collection: _PREFIX_/85/f033618.xhtml#idp9485696

Rendered MathML:

$\displaystyle=\int{\cal D}(g{\bar{A}}){\cal D}C{\cal D}{\bar{C}}\int{\cal D}\psi{\cal D}{\bar{\psi}}e^{{-\int _{0}^{{\beta}}{\mathrm{d}}\tau\int{\mathrm{d}}^{3}{\bf x}{\cal L}_{{QCD(R)}}}}.$

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