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However. as the X-ray spectrum can be considered more or less as an exponential tail to the full spectrum. a tiny shift in effective temperature or surface gravity can have a large effect to the X-ray spectrum.
However, as the X-ray spectrum can be considered more or less as an exponential tail to the full spectrum, a tiny shift in effective temperature or surface gravity can have a large effect to the X-ray spectrum.
For this reason the X-ray spectra need to be caleulated with care.
For this reason the X-ray spectra need to be calculated with care.
A potential important effect for the radiative transfer of X-ray photons in the white dwarf atmosphere is Compton scattering.
A potential important effect for the radiative transfer of X-ray photons in the white dwarf atmosphere is Compton scattering.
This was first indicated by ?. for the case of HZ 43A. Hard X-ray photons scatter many times before they reach the surface of the star. and the combined effect of all the collisions with relatively cool electrons can cause a significant energy loss for these photons. and therefore a softening of the high-energy tail of the spectrum.
This was first indicated by \citet{madej1998} for the case of HZ 43A. Hard X-ray photons scatter many times before they reach the surface of the star, and the combined effect of all the collisions with relatively cool electrons can cause a significant energy loss for these photons, and therefore a softening of the high-energy tail of the spectrum.
This effect is most noticeable at wavelengths smaller than 100A.
This effect is most noticeable at wavelengths smaller than 100.
. However. recently ? showed using a more sophisticated calculation that for both HZ 43A and Sirius B Compton scattering can be completely ignored.
However, recently \citet{suleimanov2006} showed using a more sophisticated calculation that for both HZ 43A and Sirius B Compton scattering can be completely ignored.
Therefore. in the present calculations we will also ignore Compton scattering.
Therefore, in the present calculations we will also ignore Compton scattering.
When we compared our calculations. in detail with the calculations of ?. (see Sect.
When we compared our calculations in detail with the calculations of \citet{beuermann2006} (see Sect.
5.5. for more details). we got a good agreement for HZ 43A but large differences for Sirius B in the EUV/X-ray band.
\ref{sect:comparebeuermann} for more details), we got a good agreement for HZ 43A but large differences for Sirius B in the EUV/X-ray band.
A detailed investigation of the problem showed that the differences are due to the treatment of the Lyman pseudo-continuum.
A detailed investigation of the problem showed that the differences are due to the treatment of the Lyman pseudo-continuum.
The experimental constraints on neutrino parameters al 1. 2 and 3o [L8) are given below: The observation of neutrinoless double beta (NDB) decay would signal lepton number violation and imply Majorana nature of neutrinos. for recent reviews see [19.20].
The experimental constraints on neutrino parameters at 1, 2 and $\sigma$ \cite{18} are given below: The observation of neutrinoless double beta (NDB) decay would signal lepton number violation and imply Majorana nature of neutrinos, for recent reviews see \cite{19,20}.
. The effective Majorana mass ol the electron neutrino M, which determines (he rate of NDB decay is given by Part of the Heiclelbere-Moscow collaboration claimed a signal in NDB decay corresponding to AL,=(0.11—O0.56)eV at 95%. C. EL. [21].
The effective Majorana mass of the electron neutrino $M_{ee}$ which determines the rate of NDB decay is given by Part of the Heidelberg-Moscow collaboration claimed a signal in NDB decay corresponding to $M_{ee} = (0.11 - 0.56) eV$ at $\%$ C. L. \cite{21}. .
This claim was subsequently criticized in |22].
This claim was subsequently criticized in \cite{22}.
. The results reported in (21) will be checked in the currently running and forthcoming NDB experiments.
The results reported in \cite{21} will be checked in the currently running and forthcoming NDB experiments.
Thereare large number of projects such as CUORICINO([23].. CUORE [24].. GERDA 25]. MAJORANA [26].. SuperNEMO [27].. EXO [23].. GENIUS [29] which aim lo achieve a sensilivily upto 0.01eV for M.
Thereare large number of projects such as \cite{23}, , CUORE \cite{24}, GERDA \cite{25}, MAJORANA \cite{26}, SuperNEMO \cite{27}, EXO \cite{28}, GENIUS \cite{29} which aim to achieve a sensitivity upto 0.01eV for $M_{ee}$.
In the present work. we take the upper limit ÎżáŒ± AL, to be 0.5 eV. [20].
In the present work, we take the upper limit of $M_{ee}$ to be 0.5 $eV$ \cite{20}.
. We vary the oscillation parameters within their known experimental ranges.
We vary the oscillation parameters within their known experimental ranges.
However. the Dirac-tvpe CP-violating phase 9 is varied within its full range.
However, the Dirac-type CP-violating phase $\delta$ is varied within its full range.
The two values of m4 obtained from the mass ratios p and σ. respectively must be equal to within the errors of the oscillation parameters for the simultaneous existence of (wo vanishing vanishing nimors in Ad,.
The two values of $m_1$ obtained from the mass ratios $\rho$ and $\sigma$, respectively must be equal to within the errors of the oscillation parameters for the simultaneous existence of two vanishing vanishing minors in $M_\nu$.
The first step in the numerical analvsis uses the information of the (vo known nass squared differencesalong wilh the constraint of two zero minors and large M, (o gel predictions for the mixing angles.
The first step in the numerical analysis uses the information of the two known mass squared differencesalong with the constraint of two zero minors and large $M_{ee}$ to get predictions for the mixing angles.
It is found that both the classes D; ancl Dg predict a near naximal atmospheric mixing angle while the other (wo mixing aneles remain unconstrained.
It is found that both the classes $B_5$ and $B_6$ predict a near maximal atmospheric mixing angle while the other two mixing angles remain unconstrained.
↮∏∐â†Č≀↧↮∏⊔âˆȘ⋝∖⊜↕↜≻∐≌â†Č↕⋅↕â‰șâˆąâˆâ†“â†•â‡€â†žâ†•âˆâ‰žâ‰Ÿâ‰€â†§â†Žâˆâ‰žâ‰Ÿâ†„â‰Œâ†ČâˆŁâ‡„âŠ‹âŠâŠ°âˆâ†“âˆȘ∖⇁≌â†Č⋟∖⇁ↄâˆȘâˆ–âˆ–â†œâ‰€â†§â†Žâ†•â‹…â‰Œâ‡‚âŠłâˆ–âŠœâŠŒ //4 with increasing M, as seen in Fig.(1) ≯âˆȘ↕⋅â‰șâˆąâ†„â‰€â†§âŠ”âˆ–â‡âŠłâˆ–â‡âˆâŠœâŠłâ†—â‰€â†§â†Žâˆâ‰ș⇂∏≾≟⋅⊔↕⋝↓≯âˆȘ↕⋅â‰șâˆąâ†„â‰€â†§â†Ș∖
The atmospheric mixing angle $\theta_{23}$ moves towards $\pi/4$ with increasing $M_{ee}$ as seen in Fig.(1) for class $B_5$ and Fig.(2) for class $B_6$.
âŠœâŠłâˆ–âŠœâˆâˆĄâ‹…â‹…â‹…â†ŽâŠșâˆâˆâŠłâˆ–âŠœâ‰șâˆąâ†„â‰€â†§â†Șâˆ–âŠœâŠłâˆ–â‡â‰Œâ†ČâŠłâˆ–âŠœâˆâŠœâŠłâ†—â‰€â†§â†Žâˆâ‰Œâ‡‚âˆâˆȘâˆȘ⊓∖∖↜âˆȘâˆ–â†œâ‰€â†§â†Žâˆâ†„âŠłâˆ–âŠœâˆâ†•âˆâ‰žâ‰Ÿâˆâ†“â†•âˆâˆȘâ†•â‹…âŠłâˆ–âŠœâ†•âˆâ‡€âˆȘ∣∕ â†„â‰€â†§â†ŽâŠ“âˆâ‹…â‰€â†§â†Žâˆâ‹Ąâˆ–â†œâ†•â†œâ‰»â†•â‹…â‰Œâ†Čâ‰ș∐â‰șâˆąâ†„â‰€â†§â†Žâˆâ‰Œâ†Č≀↧↮↕⋅∐↓≀↧↮⇀↾↕∐⋯↮
Thus classes $B_5$ and $B_6$ of two vanishing minors in $M_\nu$ naturally predict a near maximal atmospheric mixing angle.
ↄ≀↧↎∏⊔âˆȘ⋟∖⊜↕↜≻∐≌â†Č↕⋅↕â‰șâˆąâˆâ†“â†•â‡€â†žâ†•âˆâ‰žâ‰Ÿâ‰€â†§â†Žâˆâ‰žâ‰Ÿâ†„â‰Œâ†Č⋅ ↮âŠș∐≌â†Č⋟∖⇁≌â†Čâ‰ș∹âˆȘ∐≌⇂⋟∖⊜∩â†Čâ†•â†œâ‰»â†„â‰€â†•â†Žâ†łâ†œâ‰Œâ†Č⋟∖⇁↕∐ↄâˆȘ⋯∱â‰ș∹âˆȘ∏∐ↄ⊔∐â†Č≌â†Č⇀↞↕↜≻≌â†Č↕⋅↕∐∐â†Č∐ↄ≀↧↎ↄ↕∐↕↜≻∏ↄâˆȘ∐⊔∐â†Č⊔∐⋅≌â†Č≌â†Č∐∐⇀↾↕∐↖â‰ș↜↔↎≀↧↎∐≞≟
Thesecond step takes into account the experimental input on the three mixing angles including the recent T2K results on the reactor mixing angle.
ↄ≌â†Č⋟∖⊜↕∐â‰șâˆąâ†„â‹Żâˆâˆâ‰žâ†œâ†”â†Ž ⊔∐â†Č↕⋅≌â†Čâ‰șâˆąâ‰Œâ†Č∐ↄ↎âŠș⊋↕∖⊜↕⋅≌â†Č⋟∖⊜∏∐⋟∖⊜âˆȘ∐⊔∐â†Č↕⋅≌â†Č≀↧↮â‰șâˆąâ†„âˆȘ↕⋅∐↓↕⇀↞↕∐≞↜↔↎≀↕↎∐≞≟ↄ↩⋅↎âŠșↄ∐â†Č↕⋅≌â†Č⋟∖⊜∏
The results for $\theta_{23}$ are plotted in Fig.(3) for class $B_5$ and Fig.(4) for class $B_6$ .
∐⋟∖⊜↓↶âˆȘâ†•â‹…âˆŁâ‡„âŠ‹â‹źâŠ°â‰€â‹Żâ†Č↕↜≻ↄâˆȘ⊔≌â†Čâ‰ș⊔∐∏≾≟⋅⋖⋡⊑⊰⇄⋝ ↓≯âˆȘ↕⋅â‰șâˆąâ†„â‰€â†§âŠ”âˆ–âŠœâŠłâˆ–âŠœâˆâ†Žâ‰€â†§â†Žâˆâ‰Œâ‡‚âˆâ‰žâ‰Ÿâ‹…â‰Œâ‹âŠ„â‹â†“â‰ŻâˆȘ↕⋅â‰șâˆąâ†„â‰€â†§â†Șâˆ–â‹±âˆ–âŠœâˆâˆĄâ‹…â‹…â‹…âˆâ‹Żâ†ČↄâˆȘ⊔∐â†Č↕⋅≌â†Čↄ≀↧↎∐∖↜≌â†Čâ†„âˆĄâˆ–â‡â†„â‰€â†§â†Žâ†•â‹…â‰žâ‰Ÿâ‰Œâ†Čâˆ–â†œâ‰€â†§â†Žâ†„â‹Żâ†ČâˆȘâ†“â‹ĄâˆŁâ‡„â†“âˆ¶âŠ°â‹…âŠ”âˆâ†Č∐∐⋅≀↧↮â‰șâˆąâˆ’â†„â‹Ąâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č≌↕âŠČ↕↮ ∖⇁↕âˆȘↄ≀↧↎∐↕ↄ≞≟↕↜≻∐≀↧
Due to the relatively large value of $\theta _{13}$, the Dirac-type CP violating phase is almost fixed near $\pi/2$ or $3\pi/2$ predicting almost maximal CP violation for these textures.
⊔∖⊜≌â†Č↕⋝∖⊜≀↧↎∐⊔âˆȘâŠłâˆ–â‡â†„â‡‚âˆŽâ†“â‡€â†žâ‰Œâ†Čâ‰ș⇂∐≌â†Č≀∐⋅⊌∕∕∕⊋âˆȘ↕⋅⊑↜⊰⊌∕∕∕∃↕↜≻↕⋅≌â†Čâ‰ș∐â‰ș∱∐∐≾≟≀↧↮∐⊔âˆȘâŠłâˆ–âŠœâ†„âˆâ†“â‰€â†§â†Žâ‡€â†žâ†•âˆâ†“â‰€â†§â†ŽâŠ”â†•âŠČↄ↎∖↜↕âˆȘↄ≀↧↎∐âˆȘ∐↓⋟âˆȘ↕⋅ ⊔∐â†ČâŠłâˆ–â‡â‰Œâ†Čↄ≌â†Č⇀↞⊓∐⋅≌â†ČâŠłâˆ–âŠœâ‹…âˆâ‰žâ‰Ÿâ‹…â‹œâ‹â†±â‰»â‡„â‹â‰€â†§â†Žâˆâ‰Œâ‡‚âŠĄâ‰žâ‰Ÿâ‹…â‰Œâ‹â‰șâ‰šâ‡„â‹âŠłâˆ–âŠœâˆâˆȘ∖∖↜⊔∐â†Čâ‰ș∹
Fig.(5) and Fig.(6) show the correlation between the two Majorana-type phases and $M_{ee}$ : the phases $\alpha$ and $\beta$ approach zero with increasing $M_{ee}$ .
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰ș
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰ș∹
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰ș∱≀
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰ș∱≀↧
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰ș∱≀↧↮
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰ș∱≀↧↮∐
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰ș∱≀↧↮∐∡
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰ș∱≀↧↮∐∡∖
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰ș∱≀↧↮∐∡∖⇁
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œ
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†Č
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†Č⊳
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†Č⊳∖
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†Č⊳∖⇁
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†Č⊳∖⇁∐
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†Č⊳∖⇁∐∐
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†Č⊳∖⇁∐∐↓
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†Č⊳∖⇁∐∐↓≀
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†Č⊳∖⇁∐∐↓≀↧
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†Č⊳∖⇁∐∐↓≀↧↮
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Č
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰ș
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰ș⇂
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰ș⇂∐
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰ș⇂∐↓
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰ș⇂∐↓≀
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰ș⇂∐↓≀↧
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰ș⇂∐↓≀↧⊔
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰ș⇂∐↓≀↧⊔∖
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰ș⇂∐↓≀↧⊔∖⊜
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰șâ‡‚âˆâ†“â‰€â†§âŠ”âˆ–âŠœâŠł
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰șâ‡‚âˆâ†“â‰€â†§âŠ”âˆ–âŠœâŠłâˆ–
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰șâ‡‚âˆâ†“â‰€â†§âŠ”âˆ–âŠœâŠłâˆ–â‡
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰șâ‡‚âˆâ†“â‰€â†§âŠ”âˆ–âŠœâŠłâˆ–â‡âˆ
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰șâ‡‚âˆâ†“â‰€â†§âŠ”âˆ–âŠœâŠłâˆ–â‡âˆâ†“
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰șâ‡‚âˆâ†“â‰€â†§âŠ”âˆ–âŠœâŠłâˆ–â‡âˆâ†“â‰€
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰șâ‡‚âˆâ†“â‰€â†§âŠ”âˆ–âŠœâŠłâˆ–â‡âˆâ†“â‰€â†§
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰șâ‡‚âˆâ†“â‰€â†§âŠ”âˆ–âŠœâŠłâˆ–â‡âˆâ†“â‰€â†§â†Ž
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰șâ‡‚âˆâ†“â‰€â†§âŠ”âˆ–âŠœâŠłâˆ–â‡âˆâ†“â‰€â†§â†Žâˆ
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰șâ‡‚âˆâ†“â‰€â†§âŠ”âˆ–âŠœâŠłâˆ–â‡âˆâ†“â‰€â†§â†Žâˆâ‹…
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰șâ‡‚âˆâ†“â‰€â†§âŠ”âˆ–âŠœâŠłâˆ–â‡âˆâ†“â‰€â†§â†Žâˆâ‹…â†•
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰șâ‡‚âˆâ†“â‰€â†§âŠ”âˆ–âŠœâŠłâˆ–â‡âˆâ†“â‰€â†§â†Žâˆâ‹…â†•â‰ș
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰șâ‡‚âˆâ†“â‰€â†§âŠ”âˆ–âŠœâŠłâˆ–â‡âˆâ†“â‰€â†§â†Žâˆâ‹…â†•â‰ș∹
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰șâ‡‚âˆâ†“â‰€â†§âŠ”âˆ–âŠœâŠłâˆ–â‡âˆâ†“â‰€â†§â†Žâˆâ‹…â†•â‰șâˆąâ‰Œ
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰șâ‡‚âˆâ†“â‰€â†§âŠ”âˆ–âŠœâŠłâˆ–â‡âˆâ†“â‰€â†§â†Žâˆâ‹…â†•â‰șâˆąâ‰Œâ†Č
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰șâ‡‚âˆâ†“â‰€â†§âŠ”âˆ–âŠœâŠłâˆ–â‡âˆâ†“â‰€â†§â†Žâˆâ‹…â†•â‰șâˆąâ‰Œâ†Č⊳
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰șâ‡‚âˆâ†“â‰€â†§âŠ”âˆ–âŠœâŠłâˆ–â‡âˆâ†“â‰€â†§â†Žâˆâ‹…â†•â‰șâˆąâ‰Œâ†Č⊳∖
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰șâ‡‚âˆâ†“â‰€â†§âŠ”âˆ–âŠœâŠłâˆ–â‡âˆâ†“â‰€â†§â†Žâˆâ‹…â†•â‰șâˆąâ‰Œâ†ČâŠłâˆ–âŠœ
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰șâ‡‚âˆâ†“â‰€â†§âŠ”âˆ–âŠœâŠłâˆ–â‡âˆâ†“â‰€â†§â†Žâˆâ‹…â†•â‰șâˆąâ‰Œâ†ČâŠłâˆ–âŠœâ†“
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰șâ‡‚âˆâ†“â‰€â†§âŠ”âˆ–âŠœâŠłâˆ–â‡âˆâ†“â‰€â†§â†Žâˆâ‹…â†•â‰șâˆąâ‰Œâ†ČâŠłâˆ–âŠœâ†“â‰Ż
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰șâ‡‚âˆâ†“â‰€â†§âŠ”âˆ–âŠœâŠłâˆ–â‡âˆâ†“â‰€â†§â†Žâˆâ‹…â†•â‰șâˆąâ‰Œâ†ČâŠłâˆ–âŠœâ†“â‰ŻâˆȘ
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰șâ‡‚âˆâ†“â‰€â†§âŠ”âˆ–âŠœâŠłâˆ–â‡âˆâ†“â‰€â†§â†Žâˆâ‹…â†•â‰șâˆąâ‰Œâ†ČâŠłâˆ–âŠœâ†“â‰ŻâˆȘ↕
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰șâ‡‚âˆâ†“â‰€â†§âŠ”âˆ–âŠœâŠłâˆ–â‡âˆâ†“â‰€â†§â†Žâˆâ‹…â†•â‰șâˆąâ‰Œâ†ČâŠłâˆ–âŠœâ†“â‰ŻâˆȘ↕⋅
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰șâ‡‚âˆâ†“â‰€â†§âŠ”âˆ–âŠœâŠłâˆ–â‡âˆâ†“â‰€â†§â†Žâˆâ‹…â†•â‰șâˆąâ‰Œâ†ČâŠłâˆ–âŠœâ†“â‰ŻâˆȘ↕⋅⊔
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰șâ‡‚âˆâ†“â‰€â†§âŠ”âˆ–âŠœâŠłâˆ–â‡âˆâ†“â‰€â†§â†Žâˆâ‹…â†•â‰șâˆąâ‰Œâ†ČâŠłâˆ–âŠœâ†“â‰ŻâˆȘ↕⋅⊔∐
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰șâ‡‚âˆâ†“â‰€â†§âŠ”âˆ–âŠœâŠłâˆ–â‡âˆâ†“â‰€â†§â†Žâˆâ‹…â†•â‰șâˆąâ‰Œâ†ČâŠłâˆ–âŠœâ†“â‰ŻâˆȘ↕⋅⊔∐â†Č
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰șâ‡‚âˆâ†“â‰€â†§âŠ”âˆ–âŠœâŠłâˆ–â‡âˆâ†“â‰€â†§â†Žâˆâ‹…â†•â‰șâˆąâ‰Œâ†ČâŠłâˆ–âŠœâ†“â‰ŻâˆȘ↕⋅⊔∐â†Č↕
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰șâ‡‚âˆâ†“â‰€â†§âŠ”âˆ–âŠœâŠłâˆ–â‡âˆâ†“â‰€â†§â†Žâˆâ‹…â†•â‰șâˆąâ‰Œâ†ČâŠłâˆ–âŠœâ†“â‰ŻâˆȘ↕⋅⊔∐â†Č↕↜
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰șâ‡‚âˆâ†“â‰€â†§âŠ”âˆ–âŠœâŠłâˆ–â‡âˆâ†“â‰€â†§â†Žâˆâ‹…â†•â‰șâˆąâ‰Œâ†ČâŠłâˆ–âŠœâ†“â‰ŻâˆȘ↕⋅⊔∐â†Č↕↜≻
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰șâ‡‚âˆâ†“â‰€â†§âŠ”âˆ–âŠœâŠłâˆ–â‡âˆâ†“â‰€â†§â†Žâˆâ‹…â†•â‰șâˆąâ‰Œâ†ČâŠłâˆ–âŠœâ†“â‰ŻâˆȘ↕⋅⊔∐â†Č↕↜≻≀
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰șâ‡‚âˆâ†“â‰€â†§âŠ”âˆ–âŠœâŠłâˆ–â‡âˆâ†“â‰€â†§â†Žâˆâ‹…â†•â‰șâˆąâ‰Œâ†ČâŠłâˆ–âŠœâ†“â‰ŻâˆȘ↕⋅⊔∐â†Č↕↜≻≀↧
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰șâ‡‚âˆâ†“â‰€â†§âŠ”âˆ–âŠœâŠłâˆ–â‡âˆâ†“â‰€â†§â†Žâˆâ‹…â†•â‰șâˆąâ‰Œâ†ČâŠłâˆ–âŠœâ†“â‰ŻâˆȘ↕⋅⊔∐â†Č↕↜≻≀↧↎
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the
âˆȘ↕⋅↕⋅≌â†Čↄ≀↧↎∐âˆȘâˆâˆŁâ†œâ‰»â‰Œâ†Čↄ∖∖↜≌â†Č≌â†Č∐⊔∐â†Čↄ∖∖↜âˆȘâ‡€âˆ–â†•â‰€â†§â†Žâˆ™â†żâ‰Œâ‰»â†•â‹…â‰€â†§â†Žâˆâ‰€â†§â†Žâˆ’â†„âˆĄâˆ–â†œâ†•â†œâ‰»â‰Œâ†Č↕↜≻∐≀↧â†Ș∖⊜≌â†Č⊳∖⇁ ≀↧↮∐â‰ș⇂⇀âˆȘ⊓∶⊔∐â†Č↕↜≻∐≀↧⊔∖⊜≌â†ČâŠłâˆ–â‡âˆŁâ†œâˆŽâ‰€â†§â†Žâˆâ‰șâ‡‚â†œâ‰łâ†Ÿâ‰€â†§â†Žâ†•â†œâ‰»â†•â†œâ‰»â†•â‹…âˆȘ≀↧↮â‰șâˆąâˆâˆ â‰Œâ†Č↕⋅âˆȘ∖∖⊜ↄ⊔ↄ↕∐â‰șâˆąâ†•â‹…â‰Œâ†Č≀↧â†Ș∖⊜↕∐≞≟⇀âˆȘâŠ“â‹…â†Œâ‰šâŠłâˆ–â‡â‰€â†§â†Žâˆâ‰Œâ†Č⇀↞≀↧↎∐↓↕↜≻ↄ≌â†Č⋅∖∖↜≌â†Č∖∖↜↕⋅∐≌â†Č ⊔∐â†Č∐∏∐∐â†Č↕⋅↕â‰șâˆąâ‰€â†§â†ŽâˆâˆĄâˆ–â‡â‰Œâ†ČâŠłâˆ–â‡âˆâˆâ†“â‰€â†§â†Žâˆ©â†Čâ‰șâ‡‚âˆâ†“â‰€â†§âŠ”âˆ–âŠœâŠłâˆ–â‡âˆâ†“â‰€â†§â†Žâˆâ‹…â†•â‰șâˆąâ‰Œâ†ČâŠłâˆ–âŠœâ†“â‰ŻâˆȘ↕⋅⊔∐â†Č↕↜≻≀↧↎⊔
As an example, wewrite the numerically estimated mass matrices for thepattern $B_5$ , the matrices are obtainedfor the