Modèl Lhermite yo

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Ale nan: Navigasyon, Fouye

Modèl Lhermite yo pèmèt ke nou sentetize yon pakèt eleman oubyen opjè antre yo . Modèl Lhermite yo pèmèt sentetize...

Modèl flèch Jonatan de fason jeneral[edite | modifier le wikitexte]

1 S 20 v 20 konsène lansman flèch, nou kapab li chapit 20 an pou nou ka genyen yon meyè ide . Gen 3 posibilite lè ou lanse yon flèch.

Tout swit kwasant nonm antye kapab ekri konsa :


\mathbb{U}_n=\sum_{i=1}^{f\left(n\right)}{\left(\left[\frac{1+\sum_{m=1}^{i}{\varphi\left(m\right)}}{n+1}\right]\times\left[\frac{n+1}{1+\sum_{m=1}^{i}{\varphi\left(m\right) }}\right]\times i\times\varphi\left(i\right)\right)}

e pi jeneralman :

\mathbb{U}_n=\sum_{i=1}^{f\left(n\right)}{\left(\left[\frac{\alpha+\sum_{m=1}^{i}{\varphi\left(m\right)}}{n+\alpha}\right]\times\left[\frac{n+\alpha}{\alpha+\sum_{m=1}^{i}{\varphi\left(m\right) }}\right]\times i\times\varphi\left(i\right)\right)}


avèk f\left(n\right)\geq \mathbb{U}_n

e  \alpha >0  

Nonm premye ak modèl flèch Jonatan[edite | modifier le wikitexte]

P_n = \sum_{i=1}^{2^{2^{n}}}\left(\left\lfloor\frac {1+ \sum_{m=1}^{i}{\left( 1-\left\lfloor{\frac{\left\lfloor{\frac{\left(m!\right)^2}{m^3}}\right\rfloor}{\frac{\left(m!\right)^2}{m^3}}}\right\rfloor\right)}}{n+1}\right\rfloor\times{\left\lfloor\frac{n+1}{1+ \sum_{m=1}^{i}{\left( 1-\left\lfloor{\frac{\left\lfloor{\frac{\left(m!\right)^2}{m^3}}\right\rfloor}{\frac{\left(m!\right)^2}{m^3}}}\right\rfloor\right)}}\right\rfloor}\times{i}\times{\left({1-\left\lfloor{\frac{\left\lfloor(\frac{\left(i!\right)^2}{i^3}\right\rfloor}{\frac{\left(i!\right)^2}{i^3}}}\right\rfloor}\right)}\right)
P_n = \sum_{i=1}^{2^n}\left(\left\lfloor\frac {1+ \sum_{m=1}^{i}{\left( 1-\left\lfloor{\frac{\left\lfloor{\frac{\left(m!\right)^2}{m^3}}\right\rfloor}{\frac{\left(m!\right)^2}{m^3}}}\right\rfloor\right)}}{n+1}\right\rfloor\times{\left\lfloor\frac{n+1}{1+ \sum_{m=1}^{i}{\left( 1-\left\lfloor{\frac{\left\lfloor{\frac{\left(m!\right)^2}{m^3}}\right\rfloor}{\frac{\left(m!\right)^2}{m^3}}}\right\rfloor\right)}}\right\rfloor}\times{i}\times{\left({1-\left\lfloor{\frac{\left\lfloor(\frac{\left(i!\right)^2}{i^3}\right\rfloor}{\frac{\left(i!\right)^2}{i^3}}}\right\rfloor}\right)}\right)
P_n = \sum_{i=1}^{1+n!}\left(\left\lfloor\frac {1+ \sum_{m=1}^{i}{\left( 1-\left\lfloor{\frac{\left\lfloor{\frac{\left(m!\right)^2}{m^3}}\right\rfloor}{\frac{\left(m!\right)^2}{m^3}}}\right\rfloor\right)}}{n+1}\right\rfloor\times{\left\lfloor\frac{n+1}{1+ \sum_{m=1}^{i}{\left( 1-\left\lfloor{\frac{\left\lfloor{\frac{\left(m!\right)^2}{m^3}}\right\rfloor}{\frac{\left(m!\right)^2}{m^3}}}\right\rfloor\right)}}\right\rfloor}\times{i}\times{\left({1-\left\lfloor{\frac{\left\lfloor(\frac{\left(i!\right)^2}{i^3}\right\rfloor}{\frac{\left(i!\right)^2}{i^3}}}\right\rfloor}\right)}\right)
P_n = \sum_{i=1}^{2^n}\left(\left[\frac {1+ \sum_{m=1}^{i}{\left( 1-\left[{\frac{\left[{\frac{\left(m!\right)^2}{m^3}}\right]}{\frac{\left(m!\right)^2}{m^3}}}\right]\right)}}{n+1}\right]\times{\left[\frac{n+1}{1+ \sum_{m=1}^{i}{\left( 1-\left[{\frac{\left[{\frac{\left(m!\right)^2}{m^3}}\right]}{\frac{\left(m!\right)^2}{m^3}}}\right]\right)}}\right]}\times{i}\times{\left({1-\left[{\frac{\left[(\frac{\left(i!\right)^2}{i^3}\right]}{\frac{\left(i!\right)^2}{i^3}}}\right]}\right)}\right)
P_n = \sum_{i=1}^{2^{2^{n}}
}\left(\left[\frac {1+ \sum_{m=1}^{i}{\left( 1-\left[{\frac{\left[{\frac{\left(m!\right)^2}{m^3}}\right]}{\frac{\left(m!\right)^2}{m^3}}}\right]\right)}}{n+1}\right]\times{\left[\frac{n+1}{1+ \sum_{m=1}^{i}{\left( 1-\left[{\frac{\left[{\frac{\left(m!\right)^2}{m^3}}\right]}{\frac{\left(m!\right)^2}{m^3}}}\right]\right)}}\right]}\times{i}\times{\left({1-\left[{\frac{\left[(\frac{\left(i!\right)^2}{i^3}\right]}{\frac{\left(i!\right)^2}{i^3}}}\right]}\right)}\right)

Boul rouj ak boul ble nan kad nonm premye[edite | modifier le wikitexte]

 P_{\left(\left(1-\left[\frac{\left[\frac{\left(n!\right)^2}{n^3}\right]}{\frac{\left(n!\right)^2}{n^3}}\right]\right)\times\left(\sum_{m=1}^{n}{\left(1-\left[\frac{\left[\frac{\left(m!\right)^2}{m^3}\right]}{\frac{\left(m!\right)^2}{m^3}}\right]\right)}-i\right)+i\right)}=\left(P_i-n\right)\times\left[\frac{\left[\frac{\left(n!\right)^2}{n^3}\right]}{\frac{\left(n!\right)^2}{n^3}}\right]+n


Model flèch nan kad nonm premye annakò avèk teyorem Wilson[edite | modifier le wikitexte]

\forall n \in \mathbb{N'}
(n-1)! \equiv\ -1 \pmod n \Leftrightarrow n \in \mathbb{P}

Nou kapap avanse

\forall n \in \mathbb{N'}
\left[ \frac{\left[\frac{\left(n-1\right)!+1}{n}\right]}{\frac{\left(n-1\right)!+1}{n}}\right]=1 \Leftrightarrow n \in \mathbb{P}

li evidan

\forall n \in \mathbb{N'}
\left[ \frac{\left[\frac{\left(n-1\right)!+1}{n}\right]}{\frac{\left(n-1\right)!+1}{n}}\right]=0 \Leftrightarrow n \notin \mathbb{P}

Alo annako avek modèl Lhermite yo ak teyorèm Wilson yo, nou gen teyorem sa yo :

\forall n \in \mathbb{N^*}
\left[ \frac{\left[\frac{\left(n-1\right)!+1}{n}\right]}{\frac{\left(n-1\right)!+1}{n}}\right]-\left[\frac{1}{n}\right]=1 \Leftrightarrow n \in \mathbb{P}
\forall n \in \mathbb{N^*}
\left[ \frac{\left[\frac{\left(n-1\right)!+1}{n}\right]}{\frac{\left(n-1\right)!+1}{n}}\right]-\left[\frac{1}{n}\right]=0 \Leftrightarrow n \notin \mathbb{P}

Nou gen relasyon sa yo

\forall n \in \mathbb{N^*}
\left[ \frac{\left[\frac{\left(n-1\right)!+1}{n}\right]}{\frac{\left(n-1\right)!+1}{n}}\right]-\left[\frac{1}{n}\right]=
1-\left[\frac{\left[ {\frac{\left(n!\right)^2}{n^3}}\right]}{\frac{\left(n!\right)^2}{n^3}}\right]


an chwazi you nan fomil yo


P_n = \sum_{i=1}^{2^{2^{n}}
}\left(\left[\frac {1+ \sum_{m=1}^{i}{\left( 1-\left[{\frac{\left[{\frac{\left(m!\right)^2}{m^3}}\right]}{\frac{\left(m!\right)^2}{m^3}}}\right]\right)}}{n+1}\right]\times{\left[\frac{n+1}{1+ \sum_{m=1}^{i}{\left( 1-\left[{\frac{\left[{\frac{\left(m!\right)^2}{m^3}}\right]}{\frac{\left(m!\right)^2}{m^3}}}\right]\right)}}\right]}\times{i}\times{\left({1-\left[{\frac{\left[(\frac{\left(i!\right)^2}{i^3}\right]}{\frac{\left(i!\right)^2}{i^3}}}\right]}\right)}\right)


an ranplase

 
1-\left[\frac{\left[ {\frac{\left(n!\right)^2}{n^3}}\right]}{\frac{\left(n!\right)^2}{n^3}}\right] pa \left[ \frac{\left[\frac{\left(n-1\right)!+1}{n}\right]}{\frac{\left(n-1\right)!+1}{n}}\right]-\left[\frac{1}{n}\right]



an ranplase

 
1-\left[\frac{\left[ {\frac{\left(m!\right)^2}{m^3}}\right]}{\frac{\left(m!\right)^2}{m^3}}\right] pa \left[ \frac{\left[\frac{\left(m-1\right)!+1}{m}\right]}{\frac{\left(m-1\right)!+1}{m}}\right]-\left[\frac{1}{m}\right]

e

 
1-\left[\frac{\left[ {\frac{\left(i!\right)^2}{i^3}}\right]}{\frac{\left(i!\right)^2}{i^3}}\right] pa \left[ \frac{\left[\frac{\left(i-1\right)!+1}{i}\right]}{\frac{\left(i-1\right)!+1}{i}}\right]-\left[\frac{1}{i}\right]

Yon expresyon ekivalant se :

P_n = \sum_{i=1}^{2^{2^{n}}}{\left(\left[ \frac{1+\sum_{m=1}^i{\left(\left[\frac{\left[\frac{\left(m-1\right)!+1}{m}\right]}{\frac{\left(m-1\right)!+1}{m}}\right]-\left[\frac{1}{m}\right]\right)}}{n+1} \right]\times \left[  \frac{n+1}{1+\sum_{m=1}^i{\left(\left[\frac{\left[\frac{\left(m-1\right)!+1}{m}\right]}{\frac{\left(m-1\right)!+1}{m}}\right]-\left[\frac{1}{m}\right]\right)}} \right]\times i \times \left( \left[\frac{\left[\frac{\left(i-1\right)!+1}{i}\right]}{\frac{\left(i-1\right)!+1}{i}}\right]-\left[\frac{1}{i}\right]\right) \right) }

Boul rouj ak boul ble nan kad nonm premye annakò avèk teyorem Wilson[edite | modifier le wikitexte]

An nou fè menm bagay pou :

 P_{\left(\left(1-\left[\frac{\left[\frac{\left(n!\right)^2}{n^3}\right]}{\frac{\left(n!\right)^2}{n^3}}\right]\right)\times\left(\sum_{m=1}^{n}{\left(1-\left[\frac{\left[\frac{\left(m!\right)^2}{m^3}\right]}{\frac{\left(m!\right)^2}{m^3}}\right]\right)}-i\right)+i\right)}=\left(P_i-n\right)\times\left[\frac{\left[\frac{\left(n!\right)^2}{n^3}\right]}{\frac{\left(n!\right)^2}{n^3}}\right]+n

Boul rouj ak boul ble nan kad nonm premye Mèsèn[edite | modifier le wikitexte]

Klike sou referans lan pou ka wè youn nan fòmil yo

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Boul rouj ak boul ble nan kad nonm premye Mersèn annakò avèk teyorem Wilson[edite | modifier le wikitexte]

Fonksyon Ω annako ak model Lhermite yo[edite | modifier le wikitexte]

\Omega\left(n\right)=\sum_{j=1}^n\left({\sum_{i=1}^{n}{\left({{\left[\frac{\left[\frac{n}{i^j}\right]}{\left(\frac{n}{i^j}\right)}\right]}\times\left(1-\left[\frac{\left[\frac{\left(i!\right)^2}{i^3}\right]}{\frac{\left(i!\right)^2}{i^3}}\right]\right)}\right)}}\right)

Fonksyon Liouville ak model Lhermite yo[edite | modifier le wikitexte]

\lambda\left(n\right)=\left(-1\right)^{\left(\sum_{j=1}^n\left({\sum_{i=1}^{n}{\left({{\left[\frac{\left[\frac{n}{i^j}\right]}{\left(\frac{n}{i^j}\right)}\right]}\times\left(1-\left[\frac{\left[\frac{\left(i!\right)^2}{i^3}\right]}{\frac{\left(i!\right)^2}{i^3}}\right]\right)}\right)}}\right)\right)}


Referans[edite | modifier le wikitexte]

wè tou[edite | modifier le wikitexte]