Difference between revisions of "Elong-13-05-20"

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|style="width: 50px; height: 65px;" |(1) || <math>\frac{N_{Pol}}{N_{u}} =  \frac{ \mathcal{A} \left[ \mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u  + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u \left( 1 + DA_1 P_b P_z + A_V^d P_z + \frac{1}{2}A_{zz}P_{zz}\right) \right] t_{Pol} }{ \mathcal{A} \left[ \mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u  + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u\left( 1 + A_{PZ}P_b\right) \right] t_u} </math>
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|style="width: 50px; height: 65px;" |(1) || $\frac{N_{Pol}}{N_{u}} =  \frac{ \mathcal{A} \left[ \mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u  + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u \left( 1 + DA_1 P_b P_z + A_V^d P_z + \frac{1}{2}A_{zz}P_{zz}\right) \right] t_{Pol} }{ \mathcal{A} \left[ \mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u  + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u\left( 1 + A_{PZ}P_b\right) \right] t_u} $
 
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|style="width: 50px; height: 65px;" |(2) || <math>\frac{N_{Pol}}{N_{u}} = \left( \frac{t_{Pol}}{t_u} \right)\left[ \frac{  \mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u  + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u \left( 1 + DA_1 P_b P_z + A_V^d P_z\right)  }{  \mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u  + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u\left( 1 + A_{PZ}P_b\right) } + \frac{\mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u} {\mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u  + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u\left( 1 + A_{PZ}P_b\right) } \frac{1}{2}A_{zz}P_{zz}\right] </math>
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|style="width: 50px; height: 65px;" |(2) || $\frac{N_{Pol}}{N_{u}} = \left( \frac{t_{Pol}}{t_u} \right)\left[ \frac{  \mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u  + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u \left( 1 + DA_1 P_b P_z + A_V^d P_z\right)  }{  \mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u  + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u\left( 1 + A_{PZ}P_b\right) } + \frac{\mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u} {\mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u  + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u\left( 1 + A_{PZ}P_b\right) } \frac{1}{2}A_{zz}P_{zz}\right] $
 
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If <math>t_{Pol} \approx t_u</math> and <math>f = \frac{\mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u} {\mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u  + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u\left( 1 + A_{PZ}P_b\right) } </math>,
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If $t_{Pol} \approx t_u$ and $f = \frac{\mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u} {\mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u  + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u\left( 1 + A_{PZ}P_b\right) } $,
 
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|style="width: 50px; height: 65px;" |(3) || <math>\frac{N_{Pol}}{N_{u}} = \left[ \frac{  \mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u  + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u \left( 1 + DA_1 P_b P_z + A_V^d P_z\right)  }{  \mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u  + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u\left( 1 + A_{PZ}P_b\right) } + f \frac{1}{2}A_{zz}P_{zz}\right] </math>
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|style="width: 50px; height: 65px;" |(3) || $\frac{N_{Pol}}{N_{u}} = \left[ \frac{  \mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u  + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u \left( 1 + DA_1 P_b P_z + A_V^d P_z\right)  }{  \mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u  + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u\left( 1 + A_{PZ}P_b\right) } + f \frac{1}{2}A_{zz}P_{zz}\right] $
 
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|style="width: 50px; height: 65px;" |(4) || <math>\frac{N_{Pol}}{N_{u}} - \left[ \frac{  \mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u  + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u \left( 1 + DA_1 P_b P_z + A_V^d P_z\right)  }{  \mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u  + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u\left( 1 + A_{PZ}P_b\right) }\right]=  f \frac{1}{2}A_{zz}P_{zz}</math>
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|style="width: 50px; height: 65px;" |(4) || $\frac{N_{Pol}}{N_{u}} - \left[ \frac{  \mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u  + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u \left( 1 + DA_1 P_b P_z + A_V^d P_z\right)  }{  \mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u  + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u\left( 1 + A_{PZ}P_b\right) }\right]=  f \frac{1}{2}A_{zz}P_{zz}$
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|style="width: 50px; height: 65px;" |(5) || <math>\frac{N_{Pol}}{N_{u}} - \left[ f \left( 1 + DA_1 P_b P_z + A_V^d P_z\right)\right]=  f \frac{1}{2}A_{zz}P_{zz}</math>
 
 
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Latest revision as of 13:51, 18 October 2023

(1) $\frac{N_{Pol}}{N_{u}} = \frac{ \mathcal{A} \left[ \mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u \left( 1 + DA_1 P_b P_z + A_V^d P_z + \frac{1}{2}A_{zz}P_{zz}\right) \right] t_{Pol} }{ \mathcal{A} \left[ \mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u\left( 1 + A_{PZ}P_b\right) \right] t_u} $
(2) $\frac{N_{Pol}}{N_{u}} = \left( \frac{t_{Pol}}{t_u} \right)\left[ \frac{ \mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u \left( 1 + DA_1 P_b P_z + A_V^d P_z\right) }{ \mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u\left( 1 + A_{PZ}P_b\right) } + \frac{\mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u} {\mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u\left( 1 + A_{PZ}P_b\right) } \frac{1}{2}A_{zz}P_{zz}\right] $

If $t_{Pol} \approx t_u$ and $f = \frac{\mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u} {\mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u\left( 1 + A_{PZ}P_b\right) } $,

(3) $\frac{N_{Pol}}{N_{u}} = \left[ \frac{ \mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u \left( 1 + DA_1 P_b P_z + A_V^d P_z\right) }{ \mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u\left( 1 + A_{PZ}P_b\right) } + f \frac{1}{2}A_{zz}P_{zz}\right] $
(4) $\frac{N_{Pol}}{N_{u}} - \left[ \frac{ \mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u \left( 1 + DA_1 P_b P_z + A_V^d P_z\right) }{ \mathcal{L}_{\mathrm{He}} \sigma_{\mathrm{He}}^u + \mathcal{L}_{\mathrm{N}} \sigma_{\mathrm{N}}^u + \mathcal{L}_{\mathrm{D}}\sigma_{\mathrm{D}}^u\left( 1 + A_{PZ}P_b\right) }\right]= f \frac{1}{2}A_{zz}P_{zz}$
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