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		<title>Functional Equations and How to Solve Them</title>
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		<pubDate>Sun, 30 Oct 2011 02:46:29 +0000</pubDate>
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				<category><![CDATA[ឯកសារគណិតវិទ្យា]]></category>

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		<title>The International Law On Ballast Water</title>
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		<pubDate>Tue, 09 Aug 2011 16:47:20 +0000</pubDate>
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		<title>លំហាត់វិសមភាព</title>
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		<pubDate>Sun, 07 Aug 2011 12:47:33 +0000</pubDate>
		<dc:creator>ភុល សុវណ្ណមុនី</dc:creator>
				<category><![CDATA[ឯកសារគណិតវិទ្យា]]></category>

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			<content:encoded><![CDATA[<p>&nbsp;</p>
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		<title>លំហាត់វិសមភាព</title>
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		<pubDate>Sat, 06 Aug 2011 03:57:37 +0000</pubDate>
		<dc:creator>ភុល សុវណ្ណមុនី</dc:creator>
				<category><![CDATA[ឯកសារគណិតវិទ្យា]]></category>

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		<title>លំហាត់វិសមភាព</title>
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		<pubDate>Tue, 02 Aug 2011 09:41:54 +0000</pubDate>
		<dc:creator>ភុល សុវណ្ណមុនី</dc:creator>
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		<slash:comments>2</slash:comments>
	
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			<media:title type="html">monymath</media:title>
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			<media:title type="html">inequality1</media:title>
		</media:content>

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			<media:title type="html">inequality2</media:title>
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	</item>
		<item>
		<title></title>
		<link>http://monymath.wordpress.com/2011/06/15/464/</link>
		<comments>http://monymath.wordpress.com/2011/06/15/464/#comments</comments>
		<pubDate>Wed, 15 Jun 2011 03:28:24 +0000</pubDate>
		<dc:creator>ភុល សុវណ្ណមុនី</dc:creator>
				<category><![CDATA[ឯកសារគណិតវិទ្យា]]></category>

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		<slash:comments>3</slash:comments>
	
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			<media:title type="html">sigma</media:title>
		</media:content>
	</item>
		<item>
		<title>Vietnam 2008</title>
		<link>http://monymath.wordpress.com/2011/06/13/vietnam-2008/</link>
		<comments>http://monymath.wordpress.com/2011/06/13/vietnam-2008/#comments</comments>
		<pubDate>Mon, 13 Jun 2011 03:46:57 +0000</pubDate>
		<dc:creator>ភុល សុវណ្ណមុនី</dc:creator>
				<category><![CDATA[ឯកសារគណិតវិទ្យា]]></category>

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		<slash:comments>3</slash:comments>
	
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			<media:title type="html">monymath</media:title>
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			<media:title type="html">2008_Page_1</media:title>
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			<media:title type="html">2008_Page_2</media:title>
		</media:content>
	</item>
		<item>
		<title>វិសមភាពតូលេមី(Ptolemy’s inequality)</title>
		<link>http://monymath.wordpress.com/2011/06/07/%e1%9e%9c%e1%9e%b7%e1%9e%9f%e1%9e%98%e1%9e%97%e1%9e%b6%e1%9e%96%e1%9e%8f%e1%9e%bc%e1%9e%9b%e1%9f%81%e1%9e%98%e1%9e%b8ptolemy%e2%80%99s-inequality/</link>
		<comments>http://monymath.wordpress.com/2011/06/07/%e1%9e%9c%e1%9e%b7%e1%9e%9f%e1%9e%98%e1%9e%97%e1%9e%b6%e1%9e%96%e1%9e%8f%e1%9e%bc%e1%9e%9b%e1%9f%81%e1%9e%98%e1%9e%b8ptolemy%e2%80%99s-inequality/#comments</comments>
		<pubDate>Tue, 07 Jun 2011 04:09:40 +0000</pubDate>
		<dc:creator>ភុល សុវណ្ណមុនី</dc:creator>
				<category><![CDATA[ឯកសារគណិតវិទ្យា]]></category>

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		<description><![CDATA[​​​​​​​​​​​​​​​​​​​​​​​​                                                 ភុល​  សុវណ្ណមុនី<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=monymath.wordpress.com&amp;blog=22567514&amp;post=438&amp;subd=monymath&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p><img class="aligncenter size-medium wp-image-439" title="វិសមភាពតូលេមី(Ptolemy’s inequality) " src="http://monymath.files.wordpress.com/2011/06/in1-e1307419727649.jpg?w=423&#038;h=512" alt="" width="423" height="512" /></p>
<p>​​​​​​​​​​​​​​​​​​​​​​​​                                                 ភុល​  សុវណ្ណមុនី</p>
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		<slash:comments>1</slash:comments>
	
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			<media:title type="html">monymath</media:title>
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		<media:content url="http://monymath.files.wordpress.com/2011/06/in1-e1307419727649.jpg?w=247" medium="image">
			<media:title type="html">វិសមភាពតូលេមី(Ptolemy’s inequality) </media:title>
		</media:content>
	</item>
		<item>
		<title>ប្រៀបធៀបចំនួនលោការីត</title>
		<link>http://monymath.wordpress.com/2011/06/07/%e1%9e%94%e1%9f%92%e1%9e%9a%e1%9f%80%e1%9e%94%e1%9e%92%e1%9f%80%e1%9e%94%e1%9e%85%e1%9f%86%e1%9e%93%e1%9e%bd%e1%9e%93%e1%9e%9b%e1%9f%84%e1%9e%80%e1%9e%b6%e1%9e%9a%e1%9e%b8%e1%9e%8f/</link>
		<comments>http://monymath.wordpress.com/2011/06/07/%e1%9e%94%e1%9f%92%e1%9e%9a%e1%9f%80%e1%9e%94%e1%9e%92%e1%9f%80%e1%9e%94%e1%9e%85%e1%9f%86%e1%9e%93%e1%9e%bd%e1%9e%93%e1%9e%9b%e1%9f%84%e1%9e%80%e1%9e%b6%e1%9e%9a%e1%9e%b8%e1%9e%8f/#comments</comments>
		<pubDate>Tue, 07 Jun 2011 03:04:13 +0000</pubDate>
		<dc:creator>ភុល សុវណ្ណមុនី</dc:creator>
				<category><![CDATA[ឯកសារគណិតវិទ្យា]]></category>

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		<slash:comments>1</slash:comments>
	
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		<item>
		<title>IMO 1959 (day1)</title>
		<link>http://monymath.wordpress.com/2011/06/06/imo-1959-day1/</link>
		<comments>http://monymath.wordpress.com/2011/06/06/imo-1959-day1/#comments</comments>
		<pubDate>Mon, 06 Jun 2011 11:15:06 +0000</pubDate>
		<dc:creator>ភុល សុវណ្ណមុនី</dc:creator>
				<category><![CDATA[ឯកសារគណិតវិទ្យា]]></category>

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			<content:encoded><![CDATA[<p><img class="alignleft size-full wp-image-425" title="IMO" src="http://monymath.files.wordpress.com/2011/06/imo-e1307358848130.jpg?w=457&#038;h=604" alt="" width="457" height="604" /></p>
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		<slash:comments>1</slash:comments>
	
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			<media:title type="html">monymath</media:title>
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			<media:title type="html">IMO</media:title>
		</media:content>
	</item>
		<item>
		<title>សមីការឌីផេរ៉ង់ស្យែលប៊ែរនូយី</title>
		<link>http://monymath.wordpress.com/2011/06/03/%e1%9e%9f%e1%9e%98%e1%9e%b8%e1%9e%80%e1%9e%b6%e1%9e%9a%e1%9e%8c%e1%9e%b8%e1%9e%95%e1%9f%81%e1%9e%9a%e1%9f%89%e1%9e%84%e1%9f%8b%e1%9e%9f%e1%9f%92%e1%9e%99%e1%9f%82%e1%9e%9b%e1%9e%94%e1%9f%8a%e1%9f%82/</link>
		<comments>http://monymath.wordpress.com/2011/06/03/%e1%9e%9f%e1%9e%98%e1%9e%b8%e1%9e%80%e1%9e%b6%e1%9e%9a%e1%9e%8c%e1%9e%b8%e1%9e%95%e1%9f%81%e1%9e%9a%e1%9f%89%e1%9e%84%e1%9f%8b%e1%9e%9f%e1%9f%92%e1%9e%99%e1%9f%82%e1%9e%9b%e1%9e%94%e1%9f%8a%e1%9f%82/#comments</comments>
		<pubDate>Fri, 03 Jun 2011 10:50:55 +0000</pubDate>
		<dc:creator>ភុល សុវណ្ណមុនី</dc:creator>
				<category><![CDATA[ឯកសារគណិតវិទ្យា]]></category>

		<guid isPermaLink="false">http://monymath.wordpress.com/?p=382</guid>
		<description><![CDATA[សមីការឌីផេរ៉ងស្យែលដែលមានទំរង់ ត្រូវបានគេហៅថាសមីការឌីផេរ៉ងស្យែលប៊ែនូរយី (Bernoulli differential equation) ឬ សមីការប៊ែរនូយី ដែល​​​​​​    ដោយចែកអង្គទាំងពីរនៃសមីការនឹង    គេបាន ដោយការប្តូរអញ្ញត្តិ​ដើម្បីបំលែង​សមីការទៅជាសមីការឌីផេរ៉ង់ស្យែលលីនែអ៊ែរលំដាប់ទី១។ តាង សមីការក្លាយជា ឬ គេអាចដោះស្រាយបំលែងចុងក្រោយនេះដោយប្រើកត្តាអាំងតេក្រាល<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=monymath.wordpress.com&amp;blog=22567514&amp;post=382&amp;subd=monymath&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p><strong>សមីការឌីផេរ៉ងស្យែល</strong>ដែលមានទំរង់</p>
<p><img class="tex" src="http://upload.wikimedia.org/math/7/a/3/7a342368199b828012d54f36c827979c.png" alt="\color{blue} y'+ P(x)y = Q(x)y^n\," /></p>
<p>ត្រូវបានគេហៅថា<strong>សមីការឌីផេរ៉ងស្យែលប៊ែនូរយី</strong> (Bernoulli differential equation)</p>
<p>ឬ <strong>សមីការប៊ែរនូយី</strong> ដែល​​​​​​    <img class="tex" src="http://upload.wikimedia.org/math/0/2/d/02d58bc6a6af3d216edb54f163909951.png" alt="n \neq 1;\quad 0" width="68" height="16" /></p>
<p>ដោយចែកអង្គទាំងពីរនៃសមីការនឹង  <img class="tex" src="http://upload.wikimedia.org/math/c/5/5/c553a1506b12bdc6381e6e9e0ba8f242.png" alt="\ y^n" width="19" height="19" />  គេបាន</p>
<p><img class="tex" src="http://upload.wikimedia.org/math/7/b/8/7b8b89aacc78f25b003207c89a0f8595.png" alt="\frac{y'}{y^{n}} + \frac{P(x)}{y^{n-1}} = Q(x)" /></p>
<p>ដោយការប្តូរអញ្ញត្តិ​ដើម្បីបំលែង​សមីការទៅជាសមីការឌីផេរ៉ង់ស្យែលលីនែអ៊ែរលំដាប់ទី១។</p>
<p>តាង</p>
<p><img class="tex" src="http://upload.wikimedia.org/math/e/e/5/ee519202cd991b5b0aa479d884fdf592.png" alt="u=\frac{1}{y^{n-1}} \quad \Rightarrow \quad u'=\frac{(1-n)}{y^{n}}y'" width="248" height="43" /></p>
<p>សមីការក្លាយជា</p>
<p><img class="tex" src="http://upload.wikimedia.org/math/7/5/1/7514feb3e9a587f2b947f1bd373c537e.png" alt="\frac{u'}{1-n} + P(x)u = Q(x)" /></p>
<p>ឬ</p>
<p><img class="tex" src="http://upload.wikimedia.org/math/9/f/9/9f934ea6374fd4bf5bcd5afd714d24c3.png" alt="\ u' + (1-n)P(x)u = (1-n)Q(x)" /></p>
<p>គេអាចដោះស្រាយបំលែងចុងក្រោយនេះដោយប្រើកត្តាអាំងតេក្រាល</p>
<p><img class="tex" src="http://upload.wikimedia.org/math/1/0/f/10f3c95058b56b14822155098e3cb644.png" alt="M(x)= e^{(1-n)\int P(x)dx}" /></p>
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		<slash:comments>3</slash:comments>
	
		<media:content url="http://1.gravatar.com/avatar/11990a73eaed29e18a4bf0cef6825ece?s=96&#38;d=identicon&#38;r=G" medium="image">
			<media:title type="html">monymath</media:title>
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		<media:content url="http://upload.wikimedia.org/math/7/a/3/7a342368199b828012d54f36c827979c.png" medium="image">
			<media:title type="html">\color{blue} y'+ P(x)y = Q(x)y^n\,</media:title>
		</media:content>

		<media:content url="http://upload.wikimedia.org/math/0/2/d/02d58bc6a6af3d216edb54f163909951.png" medium="image">
			<media:title type="html">n \neq 1;\quad 0</media:title>
		</media:content>

		<media:content url="http://upload.wikimedia.org/math/c/5/5/c553a1506b12bdc6381e6e9e0ba8f242.png" medium="image">
			<media:title type="html">\ y^n</media:title>
		</media:content>

		<media:content url="http://upload.wikimedia.org/math/7/b/8/7b8b89aacc78f25b003207c89a0f8595.png" medium="image">
			<media:title type="html">\frac{y'}{y^{n}} + \frac{P(x)}{y^{n-1}} = Q(x)</media:title>
		</media:content>

		<media:content url="http://upload.wikimedia.org/math/e/e/5/ee519202cd991b5b0aa479d884fdf592.png" medium="image">
			<media:title type="html">u=\frac{1}{y^{n-1}} \quad \Rightarrow \quad u'=\frac{(1-n)}{y^{n}}y'</media:title>
		</media:content>

		<media:content url="http://upload.wikimedia.org/math/7/5/1/7514feb3e9a587f2b947f1bd373c537e.png" medium="image">
			<media:title type="html">\frac{u'}{1-n} + P(x)u = Q(x)</media:title>
		</media:content>

		<media:content url="http://upload.wikimedia.org/math/9/f/9/9f934ea6374fd4bf5bcd5afd714d24c3.png" medium="image">
			<media:title type="html">\ u' + (1-n)P(x)u = (1-n)Q(x)</media:title>
		</media:content>

		<media:content url="http://upload.wikimedia.org/math/1/0/f/10f3c95058b56b14822155098e3cb644.png" medium="image">
			<media:title type="html">M(x)= e^{(1-n)\int P(x)dx}</media:title>
		</media:content>
	</item>
		<item>
		<title>វិសមភាពនេស្ប៉ីត(Nesbitt&#8217;s inequality)</title>
		<link>http://monymath.wordpress.com/2011/06/03/%e1%9e%9c%e1%9e%b7%e1%9e%9f%e1%9e%98%e1%9e%97%e1%9e%b6%e1%9e%96%e1%9e%93%e1%9f%81%e1%9e%9f%e1%9f%92%e1%9e%94%e1%9f%89%e1%9e%b8%e1%9e%8fnesbitts-inequality/</link>
		<comments>http://monymath.wordpress.com/2011/06/03/%e1%9e%9c%e1%9e%b7%e1%9e%9f%e1%9e%98%e1%9e%97%e1%9e%b6%e1%9e%96%e1%9e%93%e1%9f%81%e1%9e%9f%e1%9f%92%e1%9e%94%e1%9f%89%e1%9e%b8%e1%9e%8fnesbitts-inequality/#comments</comments>
		<pubDate>Fri, 03 Jun 2011 10:00:03 +0000</pubDate>
		<dc:creator>ភុល សុវណ្ណមុនី</dc:creator>
				<category><![CDATA[ឯកសារគណិតវិទ្យា]]></category>

		<guid isPermaLink="false">http://monymath.wordpress.com/?p=373</guid>
		<description><![CDATA[វិសមភាពនេះចែងថាចំពោះគ្រប់ចំនួនពិត a, b និង c យើងបាន សំរាយបញ្ជាក់ យើងមានៈ យើងទាញបានៈ<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=monymath.wordpress.com&amp;blog=22567514&amp;post=373&amp;subd=monymath&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>វិសមភាពនេះចែងថាចំពោះគ្រប់ចំនួនពិត a, b និង c យើងបាន</p>
<p><img class="tex" src="http://upload.wikimedia.org/math/1/1/1/1113ce27ded7ed254af1568f3b317544.png" alt="\color{blue} \frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b}\geq\frac{3}{2}" /></p>
<h3>សំរាយបញ្ជាក់</h3>
<p>យើងមានៈ</p>
<p><img class="tex" src="http://upload.wikimedia.org/math/e/f/b/efb5b3ae5bfb431dd9b9f99974e85b40.png" alt="\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}+\frac{3}{2}=\frac{1}{2}\biggl(\frac{a+b}{b+c}+\frac{b+c}{c+a}+\frac{c+a}{a+b}+\frac{a+b}{c+a}+\frac{c+a}{b+c}+\frac{b+c}{a+b}\biggl)\geq \frac{6}{2}=3" width="515" height="38" /></p>
<p>យើងទាញបានៈ</p>
<p><img class="tex" src="http://upload.wikimedia.org/math/2/f/5/2f544f4310eb732484a91ebb97579340.png" alt="\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}\geq 3-\frac{3}{2}=\frac{3}{2}" width="271" height="38" /></p>
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		<slash:comments>1</slash:comments>
	
		<media:content url="http://1.gravatar.com/avatar/11990a73eaed29e18a4bf0cef6825ece?s=96&#38;d=identicon&#38;r=G" medium="image">
			<media:title type="html">monymath</media:title>
		</media:content>

		<media:content url="http://upload.wikimedia.org/math/1/1/1/1113ce27ded7ed254af1568f3b317544.png" medium="image">
			<media:title type="html">\color{blue} \frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b}\geq\frac{3}{2}</media:title>
		</media:content>

		<media:content url="http://upload.wikimedia.org/math/e/f/b/efb5b3ae5bfb431dd9b9f99974e85b40.png" medium="image">
			<media:title type="html">\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}+\frac{3}{2}=\frac{1}{2}\biggl(\frac{a+b}{b+c}+\frac{b+c}{c+a}+\frac{c+a}{a+b}+\frac{a+b}{c+a}+\frac{c+a}{b+c}+\frac{b+c}{a+b}\biggl)\geq \frac{6}{2}=3</media:title>
		</media:content>

		<media:content url="http://upload.wikimedia.org/math/2/f/5/2f544f4310eb732484a91ebb97579340.png" medium="image">
			<media:title type="html">\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}\geq 3-\frac{3}{2}=\frac{3}{2}</media:title>
		</media:content>
	</item>
		<item>
		<title>International Mathematical Olympiad 2009(day2)</title>
		<link>http://monymath.wordpress.com/2011/06/02/international-mathematical-olympiad-2009day2/</link>
		<comments>http://monymath.wordpress.com/2011/06/02/international-mathematical-olympiad-2009day2/#comments</comments>
		<pubDate>Thu, 02 Jun 2011 03:41:07 +0000</pubDate>
		<dc:creator>ភុល សុវណ្ណមុនី</dc:creator>
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		<title>International Mathematical Olympiad 2009(day1)</title>
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		<pubDate>Thu, 02 Jun 2011 03:39:24 +0000</pubDate>
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		<title>Cambodian IMO Team Selection Tests 2011</title>
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		<pubDate>Wed, 01 Jun 2011 04:37:15 +0000</pubDate>
		<dc:creator>ភុល សុវណ្ណមុនី</dc:creator>
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