tag:blogger.com,1999:blog-53391897274045706832024-03-21T14:54:33.234-07:00Ach_MathAch_Mathhttp://www.blogger.com/profile/03635065080431678377noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-5339189727404570683.post-50097570127553396942013-03-28T05:55:00.003-07:002013-03-28T05:55:33.183-07:00DISTRIBUSI GAMMA DAN EKSPONENSIAL<strong>A. DISTRIBUSI GAMMA DAN EKSPONENSIAL</strong><br />
Distribusi normal adalah suatu distribusi yang bisa digunakan untuk
menyelesaikan banyak permasalahan dalam bidang rekayasa dan sains. Dan
banyak lagi permasalahan yang menggunakan fungsi padat jenis lain. Dua
fungsi padat itu adalah distribusi gamma dan eksponensial.<br />
Diketahui bahwa eksponensial adalahhal penting dari distribusi gamma.
Dikarenakan mempunyai terapan yang luas. Distribusi eksponensial dan
gamma mempunyai peranan penting dalam teori antrian dan keandalan
(reliabilitas).Contohnyayaitu :Jarakantarawaktutiba di
fasilitaspelayanan (misalnya : bank, lokettiketkeretaapi,dll)
danlamanyawaktusampairusaknyasukucadangalatlistrik,
seringmenyangkutdistribusieksponensial. Hubungan antara distribusigamma
dan distribusieksponensial memungkinkan penggunaan distribusi gamma
dalam jenis persoalan yang sama.<br />
Distribusi gamma berasal dari fungsi gamma yang sudah dikenal luas
dan juga dipelajari dalam banyak bidang matematika. Sebelum membahas
distribusi gamma pertamaakan dijelaskan fungsi gamma dan beberapa
sifatnya diantaranya yaitu :<br />
<strong>Definisi 1</strong><br />
<strong> </strong><strong>Fungsi Gamma </strong>didefinisikan sebagai<br />
<div align="center">
Γ(α) =</div>
untuk α > 0<br />
Sifat-sifat penting fungsi gamma adalah:<br />
<ol>
<li>Di definisikan</li>
<li>Untuk setiap α > 1 berlaku</li>
<li>Untuk sebuah bilangan bulat positif n,</li>
</ol>
1. Bukti:<br />
Misal<br />
Karena , maka<br />
terbukti bahwa<br />
2. Dengan manipulasi kalkulus pada teknik pengintegralan, maka diperoleh:<br />
Dimana,<br />
Sehingga<br />
Denganmenggunakanrumusberulang di atas, maka:<br />
Sehingga diperoleh:<br />
<div align="center">
Dst</div>
Jika dimana n bilangan bulat positif, maka dapat dituliskan:<br />
Sekarang fungsi gamma akan dipakai dalam mendefinisikan distribusi gamma.<br />
<strong>Distribusi gamma </strong>Peubah acak kontinu x berdistribusi gamma dengan parameter , bila fungsi padatnya berbentuk<br />
f(x)=<br />
Dengan α > 0 dan β > 0<br />
Untuk beberapa nilai tertentu, distribusi gamma yang khusus dengan <strong>α=1</strong>disebut distribusi eksponensial.<br />
<strong>Distribusieksponensial</strong>Peubahacakkontinu X berdistribusieksponensial, dengan parameter β, bilafungsipadatnyaberbentuk<br />
f(x)= <strong> </strong><br />
Dengan β > 0<br />
Teorema dibawah ini dan akibatnyamemberikanrataandanvariansidistribusi gamma daneksponensial<br />
<strong>Teorema 1</strong> Rataan dan variansi distribusi gamma adalah<br />
<div align="center">
μ = αβ dan = αβ<sup>2</sup></div>
Bukti:<br />
Misalkan<br />
dan sehingga,<br />
Ambil r = 1 dan r = 2, makapersamaan di atasmenjadi<br />
Sehingga adalah:<br />
Dari dan<br />
<strong> </strong><strong>Akibat 1</strong>Rataan dan variansi distribusi eksponensial adalah<br />
<div align="center">
μ = α dan = β<sup>2</sup></div>
<br />
<strong>B</strong><strong>. PENERAPAN DISTRIBUSI EKSPONENSIAL DAN GAMMA</strong><br />
Pada bab ini akan
disajikandasarbagipenerapandistribusieksponensialdalam
“waktusamapaitiba” ataupersoalanwaktusampaikejadianPoisson.
Disiniakandiberikanilustrasikemudianditeruskandenganpembahasanperandistribusi
gamma dalampenerapanini.
Perhatikanbahwarataandistribusieksponensialadalah parameter β,
kebalikandari parameter
distribusiPoisson.DistribusiPoissontidakpunyaingatan .
Maksudnyayaitubahwaterjadinyadalamselangwaktu yang
berurutantidaksalingmempengaruhi. Parameter β yang penting adalah rataan
waktu antara kejadian. Teorikeandalan (reliabilitas) yang
menyangkutkegagalanperalatanseringmemenuhi proses Poissonini, di sini β
disebutrataanwaktuantarakegagalan. Banyakkerusakanperalatanmemenuhi
proses Poisson, dankarenaitudistribusieksponensialdapatditerapkan di
situ.<br />
Dalamcontoh berikut diberikan suatu penerapan sederhana distribusi
eksponenesial pada soal dalam keandalan. Distribusi binomial juga
ikutserta dalam penyelesaiannya.<br />
<em> </em><em>Contoh 1</em><br />
<em> </em><em> </em>Misalkan variable acak kontinu X
yang menyatakanketahanansuatubantalanpeluru (dalamribuan jam) yang
diberipembebanandinamikpadasuatuputarankerjatertentumengikutisuatudistribusi
gamma dengan α = 8 danβ = 15. Maka,
probabilitassebuahbantalanpelurudapatdigunakanselama 60 ribusampai 120
ribu jam denganpembebanandinamikpadaputarankerjatersebutadalah:<br />
<em> </em><em>Contoh 2</em><br />
Misalkan suatu system mengandung sejenis komponen yang daya tahannya dalam tahun dinyatakan oleh peubah acak <em>T</em>
yang berdistribusieksponensialdengan parameter wakturataansampaigagal β
= 5. Bilasebanyak 5 komponentersebutdipasangdalam system yang
berlainan, berapakahpeluangbahwa paling sedikit 2
masihakanberfungsipadaakhirtahunkedelapan?<br />
<em> </em><em>Jawab</em><br />
Peluang bahwa suatu komponen tertentu masih akan berfungsi setelah 8 tahun adalah<br />
<div align="center">
dt</div>
Misalkan X menyatakan bahwa suatu komponen yang
masih berfungsi setelah 8 tahun. Dengan menggunakan distribusi binomial,
diperoleh<br />
Pentingnya distribusi gamma terletak pada kenyataan bahwa
distribusiinimerupakansuatukeluargadistribusi yang
distribusilainnyamerupakanhalkhusus. Tetapi gamma
sendirimempunyaiterapanpentingdalamwaktumenunggudanteorikeandalan.
JikadistribusieksponensialmemberikanwaktusampaiterjadinyakejadianPoisson
(atauwaktuantarakejadianpoissson) makawaktu (atauruang)
terjadinyasampaisejumlahtertentukejadianPoissonterjadimerupakanpeubahacak
yang
fungsipadatnyadiberikanolehdistribusigamma.Jumlahtertentukejadianiniadalah
parameter α dalamfungsipadat gamma. Karenaitumudahdipahamibahwabila α
=1 halkhususdistribusieksponensialberlaku. Fungsipadat gamma
dapatdiperolehdarihubungannyadengan proses
Poissonmiripdengancaramemperolehfungsipadateksponensial.
Rinciannyadiserahkansebagailatihan. Berikutadalahcontoh numeric
penggunaandistribusi gamma dalampenerapanwaktumenunggu.<br />
<em> </em><em>Contoh </em><em>3</em><br />
Misalkanlah bahwa hubungan telepon tiba disuatu gerdu (sentral
memenuhi proses Poissondengan rata-rata 5 hubunganmasuk per menit.
Berapakahpeluangnyabahwasetelahsemenitberlalubaru 2
hubunganmasukkegardutadi?<br />
<em> </em><em>Jawab:</em><br />
Proses Poisson berlaku dengan waktu sampai 2 kejadian
Poissonmemenuhidistribusi gamma dengan dan . Misalkan peubah acak X
menyatakan waktu dalam menit yang berlalu sebelum 2 hubunganmasuk.
Peluang yang dicariadalah<br />
<div align="center">
dx</div>
Harinaldi, <em>Prinsip – PrinsipStatistikuntukTeknikdanSains</em>, Erlangga, Jakarta (2005)<br />
Ach_Mathhttp://www.blogger.com/profile/03635065080431678377noreply@blogger.com0tag:blogger.com,1999:blog-5339189727404570683.post-19864366856123484832013-03-21T06:45:00.000-07:002013-03-21T06:45:19.552-07:00TEOREMA WILSON<div style="text-align: left;">
Berapa sisa pembagian ini??</div>
<div style="text-align: center;">
1! dibagi 2<br />2! dibagi 3<br />4! dibagi 5<br />6! dibagi 7<br />10! dibagi 11<br />12! dibagi 13<br />dst..</div>
Lalu, apa uniknya jawaban dari soal di atas? Lihat lanjutannya di bawah.<span class="fullpost"><br />=======================================================================<br /><div style="text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhoU1W0Ok7imqF-M3XEwj28bdtd-_K4AK_8QkC2QUIwW9aPjrf6lZI4Scvptp2LqAEmvuxxJYfnY2ygUoPEuYVxPS2RxoQemLXHZAFTJhm9D7TbFT15rFOwTi9B-fHvpelT2v9uzvGqt8s/s1600-h/judul1.jpg"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5375945662884986674" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhoU1W0Ok7imqF-M3XEwj28bdtd-_K4AK_8QkC2QUIwW9aPjrf6lZI4Scvptp2LqAEmvuxxJYfnY2ygUoPEuYVxPS2RxoQemLXHZAFTJhm9D7TbFT15rFOwTi9B-fHvpelT2v9uzvGqt8s/s400/judul1.jpg" style="cursor: pointer; height: 21px; width: 210px;" /></a></div>
<br /><div style="text-align: justify;">
(Semua jawaban di atas adalah "-1".)<br /><br />Dalam
buku yang dipublikasikan tahun 1770, seorang matematikawan Inggris
Edward Waring menyatakan bahwa muridnya menemukan bahwa (p-1)!+1 habis
dibagi oleh p berapapun p yang merupakan bilangan prima. Namun, tidak
ada dari keduanya yang mampu membuktikannya. Tahun 1771, Joseph Lagrange
membuktikan teorema ini, yang selanjutnya dikenal sebagai teorema
Wilson.</div>
<br /><div style="-moz-background-clip: -moz-initial; -moz-background-inline-policy: -moz-initial; -moz-background-origin: -moz-initial; background: rgb(255, 255, 255) none repeat scroll 0% 0%; border-style: double; border-width: 4px; color: black; margin-bottom: 5px; margin-left: 40px; margin-right: 40px; padding: 5px; text-align: center;">
<span style="font-weight: bold;">Teorema Wilson</span><br />Jika <img alt="" border="0" id="BLOGGER_PHOTO_ID_5375948384391603426" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjZrEpVdi4grQnEzES1jZeUd5q8WhjCgDKTCvK2mdikoljrV8pYiz_3KYTzFN04F1TKR1aopvYt_6PXC1tqPBCI7qTw7XW2O1o4igsfgi3_ctuL1kgRFHgr9rlLiHEog3sW7TuP0YKO1fk/s400/1.gif" style="vertical-align: -4pt;" /> adalah bilangan prima, maka <img alt="" border="0" id="BLOGGER_PHOTO_ID_5375948375254044274" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikGo1lPcdTozSBRN3frpeQ7aYaVYQ-FkyxEqcEE1y81FvnCpOWsKCzFzklK_3Y-1eDW55T66-NJ1Uvp-Y7JsV8h4oqxKrprJuJaGxm53s2yxDMbNRGJfeZDoCNCifkrR9tg9KazOIb2Zg/s400/2.gif" style="vertical-align: -5pt;" /> <img alt="" border="0" id="BLOGGER_PHOTO_ID_5375948367830403890" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGdgD58IvB8r-6yc4cdmmKjEDko5p8fJ6onJM2EFY-bi6EqrbNUhjdpPHYJDi8c578vm4fW_LGbcEOd5D1dKrflE9jDcQlB0a-FZyxZJx_5RjsiKjy9zfJf_nbrdIvbmJW62ph7YD5Fls/s400/3.gif" style="vertical-align: -4pt;" /></div>
<br />=======================================================================<br /><div style="text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivNkBkcXMFPA54BvVm5BvxmwcH23objhSq7XCc2T6CJFJH1wYA92qCBHLG2X9rskIWYNXBqHT050Mjk6v6iimP0h9K2hcRw2QuewUVYq4EdGZxNtgasdMspcgGSODYcmzjCsfc9O4fuMw/s1600-h/judul2.jpg"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5375950200905886546" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivNkBkcXMFPA54BvVm5BvxmwcH23objhSq7XCc2T6CJFJH1wYA92qCBHLG2X9rskIWYNXBqHT050Mjk6v6iimP0h9K2hcRw2QuewUVYq4EdGZxNtgasdMspcgGSODYcmzjCsfc9O4fuMw/s400/judul2.jpg" style="cursor: pointer; height: 19px; width: 248px;" /></a></div>
<div style="text-align: justify;">
Tentunya, kita sudah pernah mempelajari invers modulo di post <a href="http://hendrydext.blogspot.com/2009/08/kongruensi-polinomial-dan-hensel-lemma.html">INI</a>. "a adalah invers dari b modulo c" jika <img alt="" border="0" id="BLOGGER_PHOTO_ID_5375949497765701170" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKHrIuQiLCcski6d8S-33mmNIOuOgh8j7qyHvRCdDtvNSkpE5VZNiwQm2Rk9zlNSgypz7FOEgQBI3FKIh6qV8QBagjYQZK7Nc2ysIjo-ppVqS5S3W1-es40QEqulc5lON29hG5N5mhMQc/s400/4.gif" style="vertical-align: -4pt;" />. Istilah ini akan kita pakai dalam pembuktian teorema ini.</div>
<br /><div style="-moz-background-clip: -moz-initial; -moz-background-inline-policy: -moz-initial; -moz-background-origin: -moz-initial; border-style: dotted; border-width: 4px; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; padding: 5px; text-align: justify;">
Sebelum pembuktian, kita lihat ilustrasi ide di balik pembuktian ini.<br /><br />Tentukan sisa pembagian (7-1)! dibagi 7.<br />(7-1)! = 6! = 1.2.3.4.5.6.<br />Selain 1 dan 6, maka kita akan menyusun pasangan-pasangan yang merupakan invers modulo.<br /><img alt="" border="0" id="BLOGGER_PHOTO_ID_5375951602049513234" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgukfhlCt2sBxXBXsuLIV78JEjWiHarboYvlXVdV2AU-ALxiAiXxVE3qQEvZnKlPCAc8IG0KxoKY0ykBwayhfT6_FVIfH5PDeYInumd1nVcFO1nO8Y_UnV5NBxVbGvnblGP1jx9BjMX6Sg/s400/5.gif" style="vertical-align: -4pt;" /><br /><img alt="" border="0" id="BLOGGER_PHOTO_ID_5375951593013639666" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZZS07Q4xIrwCUNC99tckYAJE2s0w3F50NrB2hPZzjLekH6XbevDv0nZKdMPKGaDFKgFIR2p8kDJAGPjcaxpye4xMlpYNIU2r3V8BOze6pUZOwL6BqiPGyYx43yA-xrPXlBzeKpiNAttA/s400/6.gif" style="vertical-align: -4pt;" /><br />Oleh karenanya, kita lakukan grouping sebagai berikut:<br />6! = 1.(2.4).(3.5).6<br />Jadi, <img alt="" border="0" id="BLOGGER_PHOTO_ID_5375957607656781778" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi4mBl9yA0N9foFXq15MdsJqgGT0znr7L_S8RuvFhJTkg1fsLm-ZwhlWgV68utngDQfzNvCUI7OWeod18u70eNGYeaOXfGVaCWbNFaJqtNqrsHAfErp_m6dZHAhKJDMG9zvI5m7cI1elD4/s400/7.gif" style="vertical-align: -5pt;" />.<br /><br />Selain mod 7, kalian juga bisa coba misalnya dengan modulo yang lain, misalnya modulo 11.<br /><img alt="" border="0" id="BLOGGER_PHOTO_ID_5375959116614881794" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyRFVNQf_hD086RXHz8Ud7bRBWQ58hRRJCsxiTabsTd9_8rgDdVemigHW1Kb7zB7IO_euvFsjGCpGsQpjaOlIPbZPsyuKk-tsZ704nGKpvW0PinbQ_s3PZJO0nFl8Wd4JpmZUT9MdMFqI/s400/8.gif" style="vertical-align: -5pt;" /><img alt="" border="0" id="BLOGGER_PHOTO_ID_5375959114463701682" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjs3UXg9W_W5g-qfDbDlAQoHwGT38sV347x7OLmiYAq9iGDV34SFnWTG3z2lZfPeHWAyNCp5DecNS0DtsWs9VmBvob-aYcnvSZkVHdZZX7kWuY8fLAWd8zcCAmgabeWzw3Hgc12kKIZ-Zo/s400/9.gif" style="vertical-align: -4pt;" /><img alt="" border="0" id="BLOGGER_PHOTO_ID_5375959106249575458" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjqZe-fH8fBstZnuWyVKO-JIP-077-jMsI4EXx2cVUxuK_94qXpLDa29SjAmTKWfTst2jAFv52eny_TOoO_kg-oGtHWLj5JnYVJ4pk7-mBVW__0TqGBzzbtGf1xP8dVJy2R_XqPckA-1Tc/s400/10.gif" style="vertical-align: -4pt;" /><img alt="" border="0" id="BLOGGER_PHOTO_ID_5375959101868009074" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMwFtbxcGi9M1qrY60lIHxkpdYuMuIzI1mHDlf6C8cyPoRGFG3BYJ70SyB96URsH-6V20RAX1eMHSWuNIk-Xc40wNcDUxWUP0yoqnn4lZs_D_pH8Mthml_Y_M8DKXc9nI5bqb-X_J-VQE/s400/11.gif" style="vertical-align: -4pt;" /></div>
<br /><span style="font-weight: bold;">BUKTI TEOREMA WILSON:</span><br />Untuk <img alt="" border="0" id="BLOGGER_PHOTO_ID_5376024788465146706" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLlhdkG9aDILmkxhYgMBT0aI0MBZYCt3BVnhmCDJb46jHi2rxyInywwk1K9SpxXvNrM2zbvt0w4AA_NuI_1ccxfXDV7uZc6SM5SUuw8sncpeGRAkRq7ZVLjbWFvxoqRC3K0zstQZQiCPw/s400/1.gif" style="vertical-align: -4pt;" />, maka <img alt="" border="0" id="BLOGGER_PHOTO_ID_5376024781293693346" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjvzDDmbxTK5riwOUBC7UN6AwjJFDt0nkTTRuQjE0-70NuP1uhmeqwivg1wEhwPJB4Mu0Ng4dqIxbdDszlva1gfsY9x12tD2a0NOUuAFHRHrgCFlTBISq3WxqFzd-LeLcd9niEV8n8HJBE/s400/2.gif" style="vertical-align: -5pt;" /> adalah benar. Jadi, teorema itu benar untuk <img alt="" border="0" id="BLOGGER_PHOTO_ID_5376024788465146706" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLlhdkG9aDILmkxhYgMBT0aI0MBZYCt3BVnhmCDJb46jHi2rxyInywwk1K9SpxXvNrM2zbvt0w4AA_NuI_1ccxfXDV7uZc6SM5SUuw8sncpeGRAkRq7ZVLjbWFvxoqRC3K0zstQZQiCPw/s400/1.gif" style="vertical-align: -4pt;" />.<br /><br />Sekarang, asumsikan <img alt="" border="0" id="BLOGGER_PHOTO_ID_5376026638925579874" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXDXG3YkkO9ZIVuUNmd05-IVOSQYtkNk5hthjrgJZjFm9pWnxhLI9wR_WFBCxvaPw9gAcyuYPgdD5W_Tm-CtqZu13orNRzjK3WM3Zu0m0XJdVQZCaeBlZXwJJ0olQB3pyZrrE3CuFIF5k/s400/3.gif" style="vertical-align: -3pt;" /> adalah bilangan prima yang lebih besar 2.<br />Dari bilangan 1,2,3,4,5,..., (p-2), (p-1), bilangan yang memiliki invers modulo p terhadap dirinya sendiri HANYA <img alt="" border="0" id="BLOGGER_PHOTO_ID_5376027075971930194" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhP3jukV5K6n6QX6j79pIlpX6kXldGA7ate3dwbwBCxdw8Pb88jD32xrQh4BgkSgE1zjEWODNZlE34iaxmx2WhVQYXuC0y951MJGC4_AmQB1gOZjqFxovY9obZwJQOj-0QBO_FZvyCKHcM/s400/4.gif" style="vertical-align: -4pt;" /> dan <img alt="" border="0" id="BLOGGER_PHOTO_ID_5376027067654086130" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLKQOlHKf1x8xSOKGRriKEdNcaG-jRZDZifVi9vi1bjF1XWVEqdWDlwBjekKlTfWA94QGyD8JGpScb5jA67F69XfynX0AaX00M_vTDA5xJKGIJIG55bGrA-Eal6iNPtA41xy5Prc-nuuQ/s400/5.gif" style="vertical-align: -5pt;" />. (Bukti ada di kotak di bawah.)<br /><br /><div style="-moz-background-clip: -moz-initial; -moz-background-inline-policy: -moz-initial; -moz-background-origin: -moz-initial; border-style: dotted; border-width: 2px; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; padding: 5px; text-align: justify;">
Kita tahu bahwa <img alt="" border="0" id="BLOGGER_PHOTO_ID_5376027075971930194" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhP3jukV5K6n6QX6j79pIlpX6kXldGA7ate3dwbwBCxdw8Pb88jD32xrQh4BgkSgE1zjEWODNZlE34iaxmx2WhVQYXuC0y951MJGC4_AmQB1gOZjqFxovY9obZwJQOj-0QBO_FZvyCKHcM/s400/4.gif" style="vertical-align: -4pt;" /> memiliki invers modulo dirinya sendiri, karena <img alt="" border="0" id="BLOGGER_PHOTO_ID_5376027708954085618" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjc_-4fPFwSvLkvZAhqjNq7NIMQBpvRHsJ21_TNSH1qNcAaUi1Wr2RrqGbz0KuSODmu4Uc8physjXD5AAAA5RpKineNoc4sT47EJVYQb7Gc34SG_2TLsW-UzVE-KEpTMnAUJZqxn9RdXJs/s400/6.gif" style="vertical-align: -4pt;" />.<br /><img alt="" border="0" id="BLOGGER_PHOTO_ID_5376027067654086130" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLKQOlHKf1x8xSOKGRriKEdNcaG-jRZDZifVi9vi1bjF1XWVEqdWDlwBjekKlTfWA94QGyD8JGpScb5jA67F69XfynX0AaX00M_vTDA5xJKGIJIG55bGrA-Eal6iNPtA41xy5Prc-nuuQ/s400/5.gif" style="vertical-align: -5pt;" /> memiliki invers modulo dirinya sendiri, karena<br /><img alt="" border="0" id="BLOGGER_PHOTO_ID_5376027697363504354" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjCdfPrYXf0UHIlF8tq9mSdPw1e4XenNcLEZ2Qtqw-edK_xBrigyOPrQzSrnBV4BWbsLHy8VepL-zFfODTWagByVZpbyIym1NOko7ngZgJit6AzjMmPmOA0rppVbcTwuPDR0FX45z5sBY8/s400/7.gif" style="vertical-align: -5pt;" />.<br /><br />Lalu bagaimana dengan bilangan selain <img alt="" border="0" id="BLOGGER_PHOTO_ID_5376027075971930194" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhP3jukV5K6n6QX6j79pIlpX6kXldGA7ate3dwbwBCxdw8Pb88jD32xrQh4BgkSgE1zjEWODNZlE34iaxmx2WhVQYXuC0y951MJGC4_AmQB1gOZjqFxovY9obZwJQOj-0QBO_FZvyCKHcM/s400/4.gif" style="vertical-align: -4pt;" /> dan <img alt="" border="0" id="BLOGGER_PHOTO_ID_5376027067654086130" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLKQOlHKf1x8xSOKGRriKEdNcaG-jRZDZifVi9vi1bjF1XWVEqdWDlwBjekKlTfWA94QGyD8JGpScb5jA67F69XfynX0AaX00M_vTDA5xJKGIJIG55bGrA-Eal6iNPtA41xy5Prc-nuuQ/s400/5.gif" style="vertical-align: -5pt;" />.<br />Seandainya <img alt="" border="0" id="BLOGGER_PHOTO_ID_5376053232827639666" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggJU9TEX18FLNNZWK9GrsHSw1aMemzHBin2z5Ku5_G92MLv3nP5_HlNuuQUWEShG2UmGYJmb_r_zfJkQSyQB47ySv7jI-Ps_vuWRZrZYIfuzYZXV05iTUBoaHqx9WtPS1Psp8TJMORMgc/s400/1.gif" style="vertical-align: -2pt;" /> adalah sembarang integer yang mempunyai invers modulo terhadap dirinya sendiri dan <img alt="" border="0" id="BLOGGER_PHOTO_ID_5376053225037413826" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqv3DfwPujHSq9pBWqUbzrGDuz5H1qcpJv_lJILyXyZdm_dfesJ3DEYAssO8dpiNMg2axTC_aHwmyHS93IqGePJvGBOACbZoGjEsjPYDvrqKWW3h1wDINwe6_VaQFuldxV-jWUnBgG1U4/s400/2.gif" style="vertical-align: -4pt;" />, maka kondisi ini harus berlaku:<br /><div style="text-align: center;">
<img alt="" border="0" id="BLOGGER_PHOTO_ID_5376055263549315442" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjf70rXg2kraYD47h_IVNv4-pHh2JC_HfWF4O5nLo-gN4FCTQ3KfYJfqqCM1i9aDxp2OS273lLpGQAgV3IazQQmO9LJXzRCQuYE3-oIECF2cVkt-dpL_4kn7wAYEj85pinvOeFdgCveLeo/s400/3.gif" style="vertical-align: -4pt;" /><br /><img alt="" border="0" id="BLOGGER_PHOTO_ID_5376055254094954530" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPkfiCkQPqGJquscJzVYAIF9fhkWBV_llW02e0XLxA3_xFXteR_Sxsn7cd_6D6picqtzGUxZKSIwWBijPplZmHvDFeHBV5AS9nfhbVSuJj9qBOsjlY9x9iVIOcYhBy_c5o4f8iI3D_9Xk/s400/4.gif" style="vertical-align: -6pt;" /><br /><img alt="" border="0" id="BLOGGER_PHOTO_ID_5376055253485478018" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAKXRx6oXr4QQ2CNsmY1JOJqZhzyfB85dYgaec3zmm8fN2fz8EY-Av0hyphenhyphennZ9g4Z12NIafy44v9Cy5Ze7W6p0DHHy0Z-zxbfmz-6VLbz4YrvXuwFNFOU97D68gWC7s8sOVLX6w1RBX13XQ/s400/5.gif" style="vertical-align: -5pt;" /><br /><img alt="" border="0" id="BLOGGER_PHOTO_ID_5376055248717577042" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEji5tDuo6ZuSItetQPodKxivtHy_x3xAISjd-CYauF_vSi46NyoSTtS3725RbIBc9jvCDAQiL8j7I4m06HCoSyiIzMgGj6jlEr0tNn-dBddvAsDrGvyRtJqTWEl7sGpjv6CaPIU0tZGMhc/s400/6.gif" style="vertical-align: -7pt;" /><br /><img alt="" border="0" id="BLOGGER_PHOTO_ID_5376055239150060210" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjY__gQd8mlUs5Fj2qJuH2W9AoDhMatFINUwCNbYhax95nTx1vI5fzRoUFAWtYHX7iq1AxLyDSdkoHD3gyGGb3u7u6mtk_MI6NTQyoYnGx5S2goijA2S3XzdTmJmOe9ztPrsSU5sITlzy0/s400/7.gif" style="vertical-align: -7pt;" /></div>
Kondisi ini ternyata berkontradiksi dengan pernyataan awal bahwa <img alt="" border="0" id="BLOGGER_PHOTO_ID_5376053225037413826" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqv3DfwPujHSq9pBWqUbzrGDuz5H1qcpJv_lJILyXyZdm_dfesJ3DEYAssO8dpiNMg2axTC_aHwmyHS93IqGePJvGBOACbZoGjEsjPYDvrqKWW3h1wDINwe6_VaQFuldxV-jWUnBgG1U4/s400/2.gif" style="vertical-align: -4pt;" />. Jadi, bilangan <img alt="" border="0" id="BLOGGER_PHOTO_ID_5376053232827639666" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggJU9TEX18FLNNZWK9GrsHSw1aMemzHBin2z5Ku5_G92MLv3nP5_HlNuuQUWEShG2UmGYJmb_r_zfJkQSyQB47ySv7jI-Ps_vuWRZrZYIfuzYZXV05iTUBoaHqx9WtPS1Psp8TJMORMgc/s400/1.gif" style="vertical-align: -2pt;" /> dalam <img alt="" border="0" id="BLOGGER_PHOTO_ID_5376053225037413826" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqv3DfwPujHSq9pBWqUbzrGDuz5H1qcpJv_lJILyXyZdm_dfesJ3DEYAssO8dpiNMg2axTC_aHwmyHS93IqGePJvGBOACbZoGjEsjPYDvrqKWW3h1wDINwe6_VaQFuldxV-jWUnBgG1U4/s400/2.gif" style="vertical-align: -4pt;" /> selalu mempunyai pasangan invers modulo dengan bilangan yang lainnya.</div>
<br />Selanjutnya, kita dapat melakukan grouping sbb:<br /><img alt="" border="0" id="BLOGGER_PHOTO_ID_5376057813068016546" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiuSviU0exvgvwHdm1HYAO5prxuPSEIbuls5tFtxD6u7r21NBwmZmQgrmMoKnpZEiYSpdk-FuMJhDxZPQewFM3opUahj41nBTFApyzzGMY905ibHsU5FroblQvuUEMMHv6BcvFersNJyww/s400/8.gif" style="vertical-align: -10pt;" /><br /><span style="color: white;">_______</span><img alt="" border="0" id="BLOGGER_PHOTO_ID_5376058185875893730" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjKAQwTjrh-Ol36pev5AAiCZwY93pHWqm41EtbnCvsQ1Hf72MT-h-s0mlD0gUKCS-Al26jIn3_gD-dBJzHg1N6xZBI9cThgiID7zR8h7OEirOhIwcV0S2TdwNFUNWdCwjQEOqZKsxpMgfc/s400/10.gif" style="vertical-align: -9pt;" /><br /><span style="color: white;">_______</span><img alt="" border="0" id="BLOGGER_PHOTO_ID_5376058176514252562" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCeBglg3XTuyQi7hHNC72HndMKCsCHLKqY5_iUUnfqF-0rHhjcCzEKXBbiW2GHvoJkNYeP1dVbNZJW7Iryg94enzw8QP9NqeIp1bGqfcvQTqW4o9ryhCD0_JQgjZAUVrPRTLHHfSx-rlk/s400/11.gif" style="vertical-align: -5pt;" /><br />Jadi, teorema Wilson pun TERBUKTI. ■<br /><br />=======================================================================<br /><div style="text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgdyx-EPipi3-JMZgiQndx5GDqM0lUruvN0yUaLNwB7V-o3NgKaREt5f_RHNwjFOGupL7-862ffeh4fuzzvY_PhTOWLSKyF2yG5NNKg94TfkGj0nJDBhppvnBwlHkj1H-Sfe5v4Am55Bcg/s1600-h/judul3.jpg"><img alt="" border="0" id="BLOGGER_PHOTO_ID_5376085448474335298" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgdyx-EPipi3-JMZgiQndx5GDqM0lUruvN0yUaLNwB7V-o3NgKaREt5f_RHNwjFOGupL7-862ffeh4fuzzvY_PhTOWLSKyF2yG5NNKg94TfkGj0nJDBhppvnBwlHkj1H-Sfe5v4Am55Bcg/s400/judul3.jpg" style="cursor: pointer; height: 18px; width: 291px;" /></a></div>
<br /><div style="-moz-background-clip: -moz-initial; -moz-background-inline-policy: -moz-initial; -moz-background-origin: -moz-initial; background: rgb(255, 255, 255) none repeat scroll 0% 0%; border-style: double; border-width: 4px; color: black; margin-bottom: 5px; margin-left: 40px; margin-right: 40px; padding: 5px; text-align: center;">
<span style="font-weight: bold;">Konverse Teorema Wilson</span><br />Jika <img alt="" border="0" id="BLOGGER_PHOTO_ID_5376086053756525426" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnsuMPv5RoFIbaIK0prIx8zfik69Av1aLVY6ifDOc3e10etN6C7cdNiBu-3N54gJEHggMnecT_ZZOeH_jGfXEdRcy8BsLDnNvPvASmFM1Kn8bGKnOFS-LBEjl1oS_1NlUV02XKIfvmhTg/s400/1.gif" style="vertical-align: -5pt;" />, maka <img alt="" border="0" id="BLOGGER_PHOTO_ID_5376086049703227122" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiS6RFiGMTBQ9fwG4Eim3ra02Iv1gm9harqlw99dMkzV87SGw8MRg21QOAbXujWIoiJXdgD5YErMkitHjMkT5CqXzxqqg143vo4p8X2fVxM6spdYJR7Dpa0-7gp5IGB6ozFnLJBRmzAIiw/s400/2.gif" style="vertical-align: -2pt;" /> adalah bilangan prima </div>
<span style="font-weight: bold;">Bukti:</span><br />Andaikan <img alt="" border="0" id="BLOGGER_PHOTO_ID_5376086049703227122" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiS6RFiGMTBQ9fwG4Eim3ra02Iv1gm9harqlw99dMkzV87SGw8MRg21QOAbXujWIoiJXdgD5YErMkitHjMkT5CqXzxqqg143vo4p8X2fVxM6spdYJR7Dpa0-7gp5IGB6ozFnLJBRmzAIiw/s400/2.gif" style="vertical-align: -2pt;" /> adalah bilangan komposit. Artinya akan terdapat bilangan <img alt="" border="0" id="BLOGGER_PHOTO_ID_5376086854709821778" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi0mcXyyCdZA6wHJFhIFm5YxeQKnM1ymTEMzztdbryjI88xI7UODd7qh_0JLqzHZ2rsAW2lboEJk2STShTK07rw9oBa5dHS31P-gzZU4_xCIPSvBdPnTbmzqe6miRvnwCcNfJ8DQoyDnuo/s400/3.gif" style="vertical-align: -2pt;" /> dimana <img alt="" border="0" id="BLOGGER_PHOTO_ID_5376086845986345170" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjoNQm1viCp-PLpOb8fkvplWitv-EEnHxw_gsXLpzzcCyH3LEZTuo_iys7lXozMg61XWizGtFAxhRNJ65_HC-d74nxYACXAo2-cNMHykitFeAoUsfkWt7Z-wos9pFvHFNCdNLtNKw8miWk/s400/4.gif" style="vertical-align: -4pt;" /> sehingga <img alt="" border="0" id="BLOGGER_PHOTO_ID_5376086842762686210" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUxkwuwBxt4XsQBjugqAChyBGfq-cK2XfEx1NogIJu9afxza-KNM3G_3SOvN8HJvEkry1pM3XO7QmtsIuMIoByV7kc8OmQu2j9T3xyRua_6uCd_-BKTjs90aaDDp40PPhVND-OpkjzbeU/s400/5.gif" style="vertical-align: -5pt;" />. Artinya, kondisi ini juga berlaku:<br /><div style="text-align: center;">
<img alt="" border="0" id="BLOGGER_PHOTO_ID_5376087285746139106" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjhSzzhxr6Uvi8kji0_E6aQhcYDSjLUim9omnP_07tmA8eaqqF845Pj6FAfYoBksHvgptAVlVeeuMcRe_RmO2D1nXnwB4OQNEuPCgkZd9WMGzs3mmZR6PA0GjPMsyYgylwvGXM4vpCmfLI/s400/6.gif" style="vertical-align: -5pt;" /> <span style="color: white;">_____</span>... (i)</div>
Selanjutnya, karena <img alt="" border="0" id="BLOGGER_PHOTO_ID_5376086053756525426" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnsuMPv5RoFIbaIK0prIx8zfik69Av1aLVY6ifDOc3e10etN6C7cdNiBu-3N54gJEHggMnecT_ZZOeH_jGfXEdRcy8BsLDnNvPvASmFM1Kn8bGKnOFS-LBEjl1oS_1NlUV02XKIfvmhTg/s400/1.gif" style="vertical-align: -5pt;" />, artinya <img alt="" border="0" id="BLOGGER_PHOTO_ID_5376087871307998978" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgrwOCgcXW4qyRrdTDfSiI1HAntOQQmCWNDJRrlN6oXunDhuhMT_Tz8drpcYas1PFXX0SaakuXcnCDj9UaETbCxGMMju9Cz33TwshyphenhyphenZnrQO_EuNCG3bejdbgCN2jLmvEu6U2FZVuzblx1c/s400/7.gif" style="vertical-align: -5pt;" />. Karena <img alt="" border="0" id="BLOGGER_PHOTO_ID_5376086842762686210" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUxkwuwBxt4XsQBjugqAChyBGfq-cK2XfEx1NogIJu9afxza-KNM3G_3SOvN8HJvEkry1pM3XO7QmtsIuMIoByV7kc8OmQu2j9T3xyRua_6uCd_-BKTjs90aaDDp40PPhVND-OpkjzbeU/s400/5.gif" style="vertical-align: -5pt;" />, maka<br /><div style="text-align: center;">
<img alt="" border="0" id="BLOGGER_PHOTO_ID_5376087865866270994" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTZ62EeghybrPLlfHRMnK9mII2Z_foyL3F7qI7tGxTPJHflwuADP_CFE6GfGdhThzxW-rSr13JNGotu-R60vlOLXGl1ZhUyt9-kgIDggb4p71YIEzrJ1M2nAGtFDG3v8bmZanJUXfvokE/s400/8.gif" style="vertical-align: -5pt;" /> <span style="color: white;">_____</span>... (ii)</div>
Dari (i) dan (ii) dapat disimpulkan bahwa:<br /><div style="text-align: center;">
<img alt="" border="0" id="BLOGGER_PHOTO_ID_5376088649958834610" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgOJXGKD_WNCxcuPBfl3HiNE-Dl4gNta_Wx59uHKIXeE989N-3TS4Wv7aarZCbYn60X5WzCvxHZPZVpPBqE2cYnWMR5qViLRnloyuavPjeehlgwsBU88EyzdlZXUTGKrrfrwfaCWbnI0oE/s400/9.gif" style="vertical-align: -5pt;" /><br /><img alt="" border="0" id="BLOGGER_PHOTO_ID_5376088638844528546" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHS1Y83aN67A0mpXA4291FZuydPLvvZXA6thlU_TacZMlp5iwiax87EGTNCruVql3mIaDGeimxV2Ofq7e1kiaR0oXGcKetxecnlr_3Z8CVVXkROtVOAR8liCObA3Y8r2aks_OnJuLt4Ew/s400/10.gif" style="vertical-align: -5pt;" /><br /><img alt="" border="0" id="BLOGGER_PHOTO_ID_5376088636809476450" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhWACnWDdHITT2ZRmzlktAGiyILxjUUYbaGuBCWTDUn9cOdP21JKgzTOBOU7Y1PDIkDuqf9whotIw9uW4JO3wNtMDcFd9jbT1_JcLcqsk7crbrKtUe5XOOdrCXy36WIm5rbpbXeU2bx2tw/s400/11.gif" style="vertical-align: -4pt;" /></div>
Padahal ini kontradiksi dengan pernyataan "<img alt="" border="0" id="BLOGGER_PHOTO_ID_5376086845986345170" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjoNQm1viCp-PLpOb8fkvplWitv-EEnHxw_gsXLpzzcCyH3LEZTuo_iys7lXozMg61XWizGtFAxhRNJ65_HC-d74nxYACXAo2-cNMHykitFeAoUsfkWt7Z-wos9pFvHFNCdNLtNKw8miWk/s400/4.gif" style="vertical-align: -4pt;" />".<br />Artinya, <img alt="" border="0" id="BLOGGER_PHOTO_ID_5376086049703227122" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiS6RFiGMTBQ9fwG4Eim3ra02Iv1gm9harqlw99dMkzV87SGw8MRg21QOAbXujWIoiJXdgD5YErMkitHjMkT5CqXzxqqg143vo4p8X2fVxM6spdYJR7Dpa0-7gp5IGB6ozFnLJBRmzAIiw/s400/2.gif" style="vertical-align: -2pt;" /> haruslah prima.<br />Konverse teorema Wilson TERBUKTI. ■<br /></span>Ach_Mathhttp://www.blogger.com/profile/03635065080431678377noreply@blogger.com0tag:blogger.com,1999:blog-5339189727404570683.post-85429942911719307562013-03-15T07:35:00.001-07:002013-03-15T07:35:15.159-07:00A Major Goal<!--[if gte mso 9]><xml>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh0sYh_XyiuolbrOQMU0vFJQzjTW6nFooo-Krn48OWwx0qPPK3lk4mWn-J262uVDUDBNoOGfQBR5X-x3MFgqQGPqRsR4IJeGfqKyDKUABspr9yd9kaURGFjyGEiIvqDDFI-DIYpWGc_VNE/s1600/FundraisingGoalMajorGiftIdea.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh0sYh_XyiuolbrOQMU0vFJQzjTW6nFooo-Krn48OWwx0qPPK3lk4mWn-J262uVDUDBNoOGfQBR5X-x3MFgqQGPqRsR4IJeGfqKyDKUABspr9yd9kaURGFjyGEiIvqDDFI-DIYpWGc_VNE/s320/FundraisingGoalMajorGiftIdea.jpg" width="300" /></a></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 150%;"><span style="mso-tab-count: 1;"> </span>In the world, people has created by Allah
with many difference although there is seven peoples in here who has
resemblance. One people is not same with another people in the world. People has
blind side and beneficience like that including me. I have a negative of side
and positive of side but I always correct about my blind-side so maybe it will
become beneficience. And I have too a best trait that differ me than the other.
My friends said that my best trait is always giving support , motivation and
never let my friend give up. Well, maybe that is one of all my best trait. If I
have a pretension, I would have to reach it and never give up till I get what I
want. I have a big confiden that it will become real althouh need time so long.
The key is just be patient and try as you can. I bealived that Allah always
beside our self and give the best for us. See the conditon approximately I
straigth to respect about it. I cant stay enjoy to see this condition if let so
long time can damage our country. This is<span style="mso-spacerun: yes;">
</span>a kindly assest the most crucial issue or problem in my local community
that caused by people who be not aware of<span style="mso-spacerun: yes;">
</span>their comunity. The basic crucial issue is attitude and behaviora that
inclined not good and imitated bad modern behavior. I think it <span style="mso-spacerun: yes;"> </span>is influenced by Globalization. </span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 150%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: IN;">It <span style="mso-spacerun: yes;"> </span>is a process of society that knows no
boundaries and can affect the life of the nation, both directly and indirectly.
Globalization is not only a challenge, but it is also an opportunity to learn
more about life in other parts of the world. Globalization is certainly an
impact to the lives of the country, including Indonesia. The impact of
globalization includes the positive and negative effects in various areas of
social life, politics, economics, and culture that will affect the values
embody the spirit of nationalism.</span><span class="hps"> </span><span class="hps"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 150%;">Nationalism</span></span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 150%;">
<span class="hps">is</span> <span class="hps">understood (</span>teaching) <span class="hps">for the</span> <span class="hps">love</span> <span class="hps">of the
nation</span> <span class="hps">and</span> <span class="hps">the state</span> <span class="hps">it self as well as</span> <span class="hps">the awareness</span> <span class="hps">of members in</span> <span class="hps">a nation</span> <span class="hps">that
is potentially</span> <span class="hps">or</span> <span class="hps">actually</span>
<span class="hps">together achieve</span>, <span class="hps">maintain</span>, <span class="hps">and devote</span> <span class="hps">the identity</span>, <span class="hps">integrity</span>, prosperity and <span class="hps">strength of the
nation</span>. Nasionalism has a closely related with Globalization. The
nasionalism of people will decrease to the nation, because globalization has
changed attitude and behavior </span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 150%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: IN;">partly of youth like as forget a lot of identity as a
nation of Indonesia, because of his lifestyle that tends to imitate western
culture, the emergence of individualism that causes indifference attitude<span style="mso-spacerun: yes;"> </span>fellow citizens etc. So as<span style="mso-spacerun: yes;"> </span>the youth of indonesia who cares about
condition of <span style="mso-spacerun: yes;"> </span>the nation, we should be embedding
and practicing religion as well as possible, studied hard to become a useful
human behavior and can distinguish right from wrong, fostering a strong
spirit of nationalism, such as the spirit of love domestic products, consider
every act so as not to hurt yourself and others, using time with useful
activities, hang out with people who are good moral and not affected the
environment and bad relationships, realizing the rule of law, implement and
enforce the law within the meaning of good faith and fair as possible. Concerned
with that indonesia will become prosperous and go foward country.<span style="mso-spacerun: yes;"> </span>So the youth of indonesia has identity that
protect the nation and<span style="mso-spacerun: yes;"> </span>preserve the
culture heritage. </span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 150%;">I think the identity of indonesian youth
is respectfull about their culture. They will do anything if their culture had
claimed by other country. Although has <span style="mso-spacerun: yes;"> </span>influenced with globalization but they still
keep the originally culture. They have a strength and<span style="mso-spacerun: yes;"> </span>a braveness to protect their culuture for
example several years ago , any a country partly of south east of asia has
claimed the culture of indonesia. Directly, the youth of indonesia<span style="mso-spacerun: yes;"> </span>respect to keep the originally culture. Thus
will growth a youth and country of indonesia that I want. A youth who can make a
good changed for indonesia , can become indonesia like peacefully country , can
compete with another country in the world and <span style="mso-spacerun: yes;"> </span>can become best country in the world.</span></div>
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<br /></div>
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<span style="mso-tab-count: 9;"> </span>By
:</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 150%; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: IN;"><span style="mso-tab-count: 8;"> </span>ACHMAD
FATONI</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 150%;"></span></div>
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<br style="mso-special-character: line-break;" />
</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 150%;"></span></div>
Ach_Mathhttp://www.blogger.com/profile/03635065080431678377noreply@blogger.com0tag:blogger.com,1999:blog-5339189727404570683.post-34901848989860829732013-03-15T07:06:00.003-07:002013-03-15T07:06:53.837-07:00Bahan Bakar Biodisel Dari Lemak Ayam <!--[if gte mso 9]><xml>
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<span lang="EN-US" style="color: black; font-family: "Verdana","sans-serif"; font-size: 10.0pt;">Para</span><span lang="EN-US" style="color: black; font-family: "Verdana","sans-serif"; font-size: 10.0pt;"> peneliti dari <a href="http://www.uark.edu/">Universitas Arkansas</a>, Amerika Serikat,
baru-baru ini berhasil menemukan sebuah proses yang dapat mengubah lemak dan <a href="http://id.wikipedia.org/wiki/Asam_lemak">asam lemak</a> rantai panjang
dari ayam menjadi bahan bakar biodisel (<a href="http://id.wikipedia.org/wiki/Biodiesel">biodiesel fuel</a>).<br />
</span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8_kaelvsQY7gyjBdVw6dWa3PH6zAaNvjVC86rVFeIVsvO3gt5SzfN4ZEE5IdtPjE2YkuX5mWRZCr8gHO8lXGWAceSNUB3-LZbNYzhF0mxbvtBxeuJnQPcaYhgEt8KumGGJgx06sEQBv8/s1600/gambar+ayam.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="281" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8_kaelvsQY7gyjBdVw6dWa3PH6zAaNvjVC86rVFeIVsvO3gt5SzfN4ZEE5IdtPjE2YkuX5mWRZCr8gHO8lXGWAceSNUB3-LZbNYzhF0mxbvtBxeuJnQPcaYhgEt8KumGGJgx06sEQBv8/s320/gambar+ayam.jpg" width="320" /></a><br /><span lang="EN-US" style="color: black; font-family: "Verdana","sans-serif"; font-size: 10.0pt;">
Proses yang mereka temukan disebut dengan Supercritical Methanol. Melalui
proses tersebut 90% lemak ayam mampu diubah menjadi biodisel.<br />
<br />
Selama dalam proses Supercritical Methanol, lemak ayam dipanaskan pada tekanan
tinggi sampai mencapai <a href="http://en.wikipedia.org/wiki/Critical_point">critical
point</a>-nya atau titik kritisnya, yaitu temperatur dan tekanan tertinggi
dimana uap dan cairan suatu zat berada dalam kondisi kesetimbangan.<br />
<br />
Selain itu, proses supercritical methanol tidak memerlukan <a href="http://id.wikipedia.org/wiki/Katalis">katalis</a> dalam proses konversi
lemak ayam menjadi biodisel sehingga menjadi lebih kompetitif secara ekonomi.</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8_kaelvsQY7gyjBdVw6dWa3PH6zAaNvjVC86rVFeIVsvO3gt5SzfN4ZEE5IdtPjE2YkuX5mWRZCr8gHO8lXGWAceSNUB3-LZbNYzhF0mxbvtBxeuJnQPcaYhgEt8KumGGJgx06sEQBv8/s1600/gambar+ayam.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><br /></a></div>
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<span lang="EN-US" style="color: black; font-family: "Verdana","sans-serif"; font-size: 10.0pt;">by ACHMAD FATONI document SMP </span><span lang="EN-US" style="color: black; font-family: "Trebuchet MS","sans-serif"; font-size: 10.0pt;"></span></div>
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Ach_Mathhttp://www.blogger.com/profile/03635065080431678377noreply@blogger.com0tag:blogger.com,1999:blog-5339189727404570683.post-18404265418225133972012-04-20T08:49:00.004-07:002012-04-20T08:49:52.231-07:00KEHIDUPANKU<!--[if gte mso 9]><xml>
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<br />
<div class="MsoNoSpacing">
By: ACHMAD FATONI</div>
<div class="MsoNoSpacing">
<br /></div>
<div class="MsoNoSpacing">
<br /></div>
<div class="MsoNoSpacing">
Aku tidak mengerti apa yang harus aku lakukan dengan
semua ini ..</div>
<div class="MsoNoSpacing">
Mungkinkah kan menjadi seperti ini untuk selamanya....</div>
<div class="MsoNoSpacing">
Aku tak ingin menjadi seperti ini...</div>
<div class="MsoNoSpacing">
Aku ingin bebas layaknya burung-burung yang bertebangan
tanpa pemburu ....</div>
<div class="MsoNoSpacing">
Aku<span style="mso-spacerun: yes;"> </span>juga ingin
merasakan kebahagiaan yang menjadi idaman bagi setiap orang...</div>
<div class="MsoNoSpacing">
Aku ingin kehidupan berpaling kepadaku....</div>
<div class="MsoNoSpacing">
Tapi tak mungkin.......</div>
<div class="MsoNoSpacing">
Aku jalani kehidupan yang<span style="mso-spacerun: yes;">
</span>membuat aku sakit sendiri.....</div>
<div class="MsoNoSpacing">
Rasanya<span style="mso-spacerun: yes;"> </span>sulit
melepas rasa ini....</div>
<div class="MsoNoSpacing">
Rasa yang tak sewajarnya ku miliki...</div>
<div class="MsoNoSpacing">
Rasa yang mampu menusuk hati...</div>
<div class="MsoNoSpacing">
Rasa yang belum bisa aku hindari....</div>
<div class="MsoNoSpacing">
Sedih..susah..kecewa dengan semua ini..</div>
<div class="MsoNoSpacing">
Aku ingin lari dari semua ini...</div>
<div class="MsoNoSpacing">
Pergi..pergi...keluar...keluar...</div>
<div class="MsoNoSpacing">
Mencari hidupku<span style="mso-spacerun: yes;">
</span>yang sebenarnya telah pergi....</div>
<div class="MsoNoSpacing">
Aku harus bisa jalani ini....</div>
<div class="MsoNoSpacing">
Meskipun menggores hati...</div>Ach_Mathhttp://www.blogger.com/profile/03635065080431678377noreply@blogger.com0