~yummyyhamme~

4.30.2006

math..

Manong isaw at UP student:

MI: anu sa iyo?

S: 3x-5 where x=6...

MI: so 13, bale, mura lang... 5sin90 ang isa..

S: hhhmmm..pki convert naman po using arctangent...

MI: d q keri e, tangent na lang... 5tan45... kung gs2 mo mag-apply ka na lang ng reduction formula...

S: okay na po.. eto bayad... (2x^2-5x+4)/13x where x=6.923... keep the change...

~~~ganyan ka-useful ang math sa buhay natin....=p

================

haha! ala lang...txt yan sken from a friend... na-amuse lang ako... (oo, alam kho, ang babaw ko talaga kahit kelan...)...pero kc naman... bsta natuwa lang ako s idea n gs2ng palabasin ng text... ang use ng math s buhay natin...

bata pa kasi ako, winawonder ko na talaga ang use ng mga ganyang klase ng math s buhay ng isang tao... gnyan naman kc cguro ang madalas n tanong ng mga estudyante dba? bkit ba kelangan pang aralin ang masakit s ulong trigo at pamatay na algebra...

although ngaun, naappreciate q n ang existence nya dahil nagagamit q xa s physics... hndi q p rn maicp ang gamit nya s mga simple situations in lyf.. hehe..

4.29.2006

think...before you drink...

since its summer, mabili nnman ang mga softdrinks... kht aq ay sobra nanamang naadik dun...
just wanna share this message from a frend about softdrinks..

COKE or PEPSI ???

Have a look at the wrapper on a Coca Cola or Pepsi Cola 1.5 litre bottle and in the ingredients label you will find phosphoric acid in it. Minute quantities of ethylene glycol is also used (which is acknowledged in the soft drink world for making it really chill"). This is popularly known as anti-freeze which prevents water from freezing at 0 degree C and instead drops it by 4-5 degrees with minute quantities. This chemical is a known slow poison in the caliber of arsenic.

So, if you manage to drink about 4 liters of Coke or Pepsi within an hour or so, you can die.

Read along and give up these dangerous things. Be natural, have flavoured milks, butter milk and plain water instead of these "soft" drinks.

Guess what's the pH for soft drinks, e.g. Coke and Pepsi ? pH 3.4! This acidity is strong enough to dissolve teeth and bones! Our human body stops building bones at the age of about 30. Soft drinks do not have any nutrition value (in terms of vitamins &minerals). It is high in sugar content, carbonic acid, chemicals i.e. colorings etc.

Some like to take cold soft drinks after each meal. Guess what's the impact?

Our body needs an optimum temperature of 37 degrees Celsius for digestive enzyme functioning. The temperature of cold soft drinks is very much below 37 degrees or even close to 0 degrees Celsius. This will dilute the enzymes & stress the digestive system.

The food taken will not be digested. In fact it will be fermented! The fermented food produces gases, decays and becomes toxin, and gets absorbed by the intestine, circulates in the blood stream and is carried to the whole body. Hence, toxin is cumulated in other parts of the body, developing into various diseases.

Think before you drink Coke or Pepsi (or any soft drink) again.

Have you ever thought what you drink when you drink an aerated drink?

You gulp down carbon dioxide, when nobody in the world would advise you to drink CO2.

Two months back, there was a competition at DelhiUniversity. "Who could drink the most Coke?" The winner drank 8 bottles and fainted on the spot, too much CO2 in the blood. Thereafter, the principal banned all soft drinks from the college canteen!

While this might have been an extreme measure, the results do provide some food for thought. Did you know that soft drinks use chemicals in them that cause immense harm to you. Someone put a broken tooth in a bottle of Pepsi and in 10 days it DISSOLVED! Can you believe it? Teeth and bones are the only human parts that stay intact for years after death. Imagine what the drink must be doing to your soft intestines and stomach lining!

.....well, i'm sorry for d coke and pepsi manufacturers...

but these infos aren't just for pepsi and coke, it generally pertains to any other softdrinks around...

so before you drink... think first!!

....pero sayang! summer pa naman ngaun at nakaka-uhaw!!!!...=p

4.28.2006

Laguerre....

In mathematics, the Laguerre polynomials, named after Edmond Laguerre (1834 - 1886), are a polynomial sequence defined by

$L_n(x)=\frac{e^x}{n!}\frac{d^n}{dx^n}\left(e^{-x} x^n\right).$

These polynomials are orthogonal to each other with respect to the inner product given by

$\langle f,g \rangle = \int_0^\infty f(x) g(x) e^{-x}\,dx.$

Also, for each n, L_n(x) is a solution of Laguerre's equation

$(x D^2 + (1 - x) D + n) \, y(x) = 0$

which is a second-order linear differential equation with variable coefficients.

The first few polynomials are:

$L_0(x)=1\,$

$L_1(x)=-x+1\,$

$L_2(x)=\frac{1}{2}(x^2-4x+2)$

$L_3(x)=\frac{1}{6}(-x^3+9x^2-18x+6)$

$L_4(x)=\frac{1}{24}(x^4-16x^3+72x^2-96x+24)$

$L_5(x)=\frac{1}{120}(-x^5+25x^4-200x^3+600x^2-600x+120)$

$L_6(x)=\frac{1}{720}(x^6-36x^5+450x^4-2400x^3+5400x^2-4320x+720)$
and is given by the graph:

The polynomials may be expressed in terms of a contour integral

$L_n(x)=\frac{1}{2\pi i}\oint\frac{e^{-xt/(1-t)}}{(1-t)\,t^{n+1}} \; dt$

where the contour circles the origin once in a counterclockwise direction.

These are also sometimes called the associated Laguerre polynomials. The simple Laguerre polynomials are recovered from the generalized polynomials by setting α=0:

$L^{(0)}_n(x)=L_n(x).$

The associated Laguerre polynomials are orthogonal over $[0,\infty)$ with respect to the weighting function $x α e - x$ :

$\int_0^{\infty}e^{-x}x^\alpha L_n^{(\alpha)}(x)L_m^{(\alpha)}(x)dx=\frac{\Gamma(n+\alpha+1)}{n!}\delta_{nm}.$

The associated Laguerre polynomials obey the following differential equation

$x L_n^{(\alpha) \prime\prime}(x) + (\alpha+1-x)L_n^{(\alpha)\prime}(x) + n L_n^{(\alpha)}(x)=0.\,$

For integer α the defining equation above can be written as

$L_n^{(m)}(x)= (-1)^m{d^m \over dx^m} L_{n+m}(x).$

Relation to Hermite polynomials

The generalized Laguerre polynomials arise in the treatment of the quantum harmonic oscillator, due to their relation to the Hermite polynomials, which can be expressed as

$H_{2n}(x) = (-1)^n 2^{2n} n! L_n^{(-1/2)} (x^2)$

and

$H_{2n+1}(x) = (-1)^n 2^{2n+1} n! x L_n^{(1/2)} (x^2)$

where the $H n (x)$ are the Hermite polynomials.

===============================
ayan! yan ang Laguerre! isa syang special function na una kong narinig mula s aming physics 112 prof n c sir galapon...

grabe...

biruin nyo, may relasyon p pala xa kay pareng Hermite... ("er-mit" ang pagpronounce ayon kay APAPF president... hehehe..)

hndi ko yan makakalimutan....

dinerive q sa loob ng halos isang araw s lib ang recurrence relation nyan n given by:

•

ibibigay ko ang derivation nyan some other time...

pero grabe... hnding hndi ko yta makakalimutan yan sa lahat ng functions.... dahil kht nagbabad kmi s lib ng isang buong araw para magderive ng mga representation ng iba't ibang functions (hndi lang Laguerre, may bessel, legandre, hermite, at mga associated nila..), hndi p rn enough un!

toka p naman sklen ang rodrigues representation nyan, which is, unfortunately, hndi ko nderive...

e malas! nilabas s exam (finals pa!)... yan tuloy, hndi ko nasagot..

sayang!!

but eniweiz.... at least tapos nah yon...

gs2 ko lang balikan...

ang mahal kong so Laguerre....

4.27.2006

wanboringdey...

Grabe.. matatapos n pala ang april.. ang bilis ng panahon...

Malapit na birthday kho!!

kelangan na magtago.. hahahaha!!

wala akong magawa ngaun... gs2 ko mag-aral ng physics pero lagi naman me tinatamad.. huhu...

at wala rn akong masulat ngaun..

kc nga tinatamad ako gumawa ng kahit na ano...

kainis! down ang server ng tantra, hndi 2loy aq makapaglaro...

kagabi pala mag binabasa akong story, What I Did For Love ung title.. actually nabasa q na xa... binasa q lng ulit... at for d second time, naiyak ulit aq.... actually, maganda ung story khit maxadong good to be true, pero dahil story lng xa, edi patulan na at lubos-lubosin... ayan tuloy, umiyak ulit ako.. hehehe... basahin nyo rin.. ahihi..

hay grabe... SA nga pala aq ng SPP, pero feelng q mnsan parang ala lng, pmpnta lng ako pag gs2 q, nahihiya nga rn me mnsan e.... pero kc, khit n sandamakmak ung files n inuupload q.. ayun! ok p naman at relatively, marami kming nagagawa.... last day n nga pla nung isang SA knina, ung last year's SA, shocks! mejo naeexcite n rn me s congress n gaganapin s davao s october, un ung isa s mga advantage ng isang SA, nakakatravel na, all expense paid pa.. hehehe...

hay. ala tlga aq s mood ngaun...

ewan q ba...

4.21.2006

nagbabalik....

Ayan! nagbabalik na akho... ang tagal kong d n nagppost d2...nagbabasa p kaya ang mga dating nagbabasa o hndi na dahil akala nila ay patay na ang blog na 'to? well... buhay ulit akho!! hahaha!

e bakit nga ba ngaun lang ulet aq... actually..there are some few reasonses....

(1) kc tinatamad aq.. nakakatamad na kaya gumawa ng post na alam ko naman na walang sense... puro lng naman bluff ang mga pinag-sasasabi kho d2 e..dba? nakakasawa na...laging tungkol sa super duper boring life kho....

(2) bc sa acads... yan ang malupit!! pero half-true lang yan, pero infairness, i've been busy dn tlaga lalo na nitong mga huling araw ng class namin... as in chem 17 and physics 112 ba naman in one semester e! gud luck! galapon and ratilla... buti na lang MTh c galapon at TF naman c ma'm ratilla, pahinga pag wednesday at weekends... pero at least tapos nah...

so.... nagbabalik akho dahil bakasyon nah... after 3 months... hahaha! actually within just 3 months marami na ring nangyari... mga issue, mga taong biglang nakilala... (parang lagi naman 'to a!).. mga taong kinakalimutan nah... (pero parang hndi pa e! haaiizzz...)...

haaaiiizzz...napag-icp-icp kho lang...3rd year na pala akho next year! (this june..) at..oh well! ang bilis ng panahon....**sori ha? hang-over b 'to ng NIP recog knina**... paratng n ung most stressful sem "daw" namin which is next sem, marami nang major physics subject and most of all, mag-aapply na kami ng lab which is ayoko pa talaga icpin kc kinakabahan talaga akho... hhaaaiiizzzz.... parang ang sarap gumraduate noh? parang nakahinga ka nah... kanina nga, habang pinapanood ko ung nga ggraduate parang sabi q, buti pa cla.. tapos na.. although alam q there are bigger responsibilities na ahead of them pero parang at least tapos na nila ung isa s pinakaimportanteng chapter ng life ng isang tao, ang college and having a degree... parang isang malaking achievement kc para sken ang paggraduate e which is sana mangyari din sken... although i know naman mangyayari un if i will do my best! pero nakakatakot p rin e! natatakot talaga akho...

oh well.. tama nah...

haiiizzzz...dami q iniicp...bakasyon naman... dapat nagpapahinga akho a! it's time to rest... pero minsan parang hndi rn akho sanay ng wala talagang ginagawa... haaayyy!! i miss my kuya... s kanya q lang kc nabubuhos ang mga angst q s studies and s life pero 1 week n xa ala d2 s hauz... haaayyy... ni hndi ko man lang nkwento s kanya personally na pumasa aq s 112 although touched naman aq kc paalis n xa, naghihintay ng plane, ngttxt p rn xa sken kung musta grades q...hahaha! miss q n talaga un...

haaayyy...yoko na..drama nanaman...

you have come to my life through the door...

4.30.2006

math..

4.29.2006

think...before you drink...

4.28.2006

Laguerre....

Relation to Hermite polynomials

4.27.2006

wanboringdey...

4.21.2006

nagbabalik....

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