Digital explorations

It is that time of the year to upgrade the Ubuntu operating system-11.10-Oneiric Ocelot to 12.04-Precise Pangolin

May 9th, 2012

Draft mode until this notice is removed.

I do not immediately upgrade my Ubuntu system using software system upgrade. You will be at the mercy of network glitches and suffer longer times than downloading the newest ISO. Here is my terminal command for my 64 bit system:

wget -ct 0 http://ftp.ticklers.org/releases.ubuntu.org/releases//precise/ubuntu-12.04-desktop-amd64.iso

It took 3 hours and 23 minutes for the full download of 732,213,248 bytes at about 66Kbits per second speeds . That is how slow the Internet is in the Philippines.

Now you can burn the image file to a DVD or a high capacity CD disk. But we will continue to explain how to do it using a usb flash drive.

In the next step we use netbootin, a utility which installs operating systems given its ISO to usb flash drives. If not available, install it via the "sudo apt-get install unetbootin". Fire the unetbootin and specify diskimage. click on the "..." button to open a graphical menu to select the downloaded iso file. After selectiong the iso image file, click the Ok button. Then it will ask you to reboot. Save any intermediate task works if you have not done so.

You then click the reboot button and take off from there!

To be continued.

Humor in the classroom. Getting fried by an excuse.

May 7th, 2012

Subject: Fw: Why Planning is important ?

Dear friends

Some time planning is more important than hard work....,Read this ..Why Planning is important?

One Night 4 college students were playing till late night and could not study for the test which was scheduled for the next day.

In the morning they thought of a plan. They made themselves look dirty with grease and dirt. They then went up to the Dean and said that they had gone out to a wedding last night and on their return the tire of their car burst and they had to push the car all the way back and that they were in no condition to appear for the test. So the Dean said they could have the re-test after 3 days. They thanked him and said they would be ready by that time.

On the third day they appeared before the Dean. The Dean said that as this was a Special Condition Test, all four were required to sit in separate classrooms for the test. They all agreed as they had prepared well in the last 3 days.

The Test consisted of 2 questions with a total of 100 Marks.

Scroll Below for the question Paper

Q.1. Name of the car??
........... ............ ......... (2 MARKS)

Q.2. which tire burst? (98 MARKS)

a) Front Left b) Front Right
c) Back Left d) Back Right

True story from the Indian Institute of Technology Bombay ... a world class Technology university, and copied from a Facebook posting.

Posted in Humor | Click for Comments »

Avoid clicking on links to Facebook Games

April 29th, 2012

You might lose your privacy, and may provide hackers an outlet to get your passwords to sensitive sites (they are not forthcoming). This one is on Hidden Chronicles.

There are two buttons "ALLOW" and "DONT ALLOW". Now that you know, play it safe, by not making it easy for identity theft to happen. Your personal information is precious, do you want to give it away for free??!

Posted in Dangerous Internet | Click for Comments »

The Lyric mobile spam and scam

April 26th, 2012

From time to time we gat spam from 8070 with irritating messages like these (Two exmaples out of twenty stored in my phone are shown below) :

LYRIC: Manalo ng up to 20,000.00
Q: CUESHE: Lagi na lang ________, UMUULAN ba ang sunod?
Repy w/ LYRIC Y or LYRIC N now. To quit, txt OFF to 8070. P2.5/tx. prome from 01/21/12 to 01/21/13. DTINCRPermit#0400S of 12. Cflyr4dtls.

Received 09:31:32AM Today [April 26]
From: (no name)
8070

LYRIC: Manalo ng up to 20,000.00
Q: JIMMY BONDOC: Let me be the one to ________ it up, BREAK ba ang sunod?
Repy w/ LYRIC Y or LYRIC N now. To quit, txt OFF to 8070. P2.5/tx. prome from 01/21/12 to 01/21/13. DTINCRPermit#0400S of 12. Cflyr4dtls.

Received 08:3617am [April 13]
From: (no name)
8070

I just wish there is a system that someone sending unwanted message to me will be charged 2.50 pesos!

Posted in Scams, Spam | Click for Comments »

"A scam in the name of the United Nations Human Settlements Programme" Redux

April 26th, 2012

I got this new comment from a certain Kimberly regarding the posting on a scam using an international organization name.

A new comment on the post "A scam in the name of the United Nations Human Settlements Programme" is waiting for your approval:

http://adorio-research.org/wordpress/?p=12271

Author : Kimberly (IP: 208.54.39.180 , mb42736d0.tmodns.net)
E-mail : Kimkeepit100@aol.com
URL :
Whois : http://whois.arin.net/rest/ip/208.54.39.180
Comment:
After much attempts to reach you on phone, I deemed it necessary and urgent to contact you via your e-mail and to notify you finally about your outstanding compensation payment.

During our last annual calculation of your banking and Internet activities we realized that you are eligible to receive a compensation payment of $2,811,041.00 USD.

This compensation is being made to all of you who have suffered losses as a result of fraud, accident or illness.

For more information, contact the UPS agent for the delivery of your cashier check ($2,811,041.00 USD).

United Parcel Service (UPS)
Contact Name: Ford Hamilton
Tel: +2348077932717
E-mail: upscss1@aim.com

Please take note that you will pay a shipping/handling fee of $145.00 USD to UPS.

Thanks for your patience.

Tylor Robinson

Programme Manager
United Nations Human Settlements Program

Posted in Scams, Spam | Click for Comments »

repost: Complex trigonometric and hyperbolic functions

April 24th, 2012

This article originally appeared in our alternate site Optimal Learning Systems.

Complex Trigonometic Functions

$\begin{array}{ll} \hline\mbox{\bf Function }& \mbox{\bf Formula} \\ \hline\mbox{sine} & \sin(z) = \frac{1}{2j}(e^{jz} - e ^{-jz}) \\ & = \sin x \cosh y + j \cos(x) \sinh(y) \\\mbox{cosine}& \cos(z) = \frac{1}{2j}(e^{jz} + e ^{-jz}) \\ & = \cos x \cosh y - j \sin(x) \sinh(y) \\\mbox{tangent}& \tan(z) = \frac{\sin(z) }{\cos(z)}\\ &= \frac{e^{jz} - e^{-jz}}{j(e^{jz} + e^{-jz})} \\\mbox{cotangent}& \cot(z) = \frac{\cos(z)} {sin(z)}\\ &= \frac{j(e^{jz} + e^{-jz}}{e^{jz} - e^{-jz}} \\\mbox{secant} & \sec(z) = \frac{1}{\cos(z)} = \frac{2}{e^{jz} + e^{-jz}}\\\mbox{cosecant} &\csc(z) = \frac{1}{\sin(z)} = \frac{2j }{e^{jz} - e^{-{jz}}}\\\end{array}$

Complex Hyperbolic Functions.

$\begin{array}{ll} \hline\mbox{\bf Function} & \mbox{\bf Formula}\\ \hline\mbox{hyperbolic sine} & \sinh(z)= \frac{e^{jz}- e ^{-jz}}{2} = -j \sin(jz)\\ &= \sinh(x) \cos(y) + j \cosh(x) \sin(y)\\\mbox{hyperbolic cosine}& \cosh(z) = \frac{e^{jz}+ e ^{-jz}}{2} = \cos(jz)\\\mbox{hyperbolic tangent} & \tanh(z) = \frac{\sinh(z)}{\cosh(z)} = \frac{e^z - e^{-z}}{e^z + e^{-z}}\\ \mbox{hyperbolic secant} &sech(z) = \frac{1}{\cosh(z)} = \frac{2}{e^z + e^{-z}}\\\mbox{hyperbolic cosecant} & csch(z)= \frac{1}{\sinh(z)} = \frac{2}{e^z - e^{-z}}\\\mbox{hyperbolic cotangent} &\coth(z) = \frac{\cosh(z)}{\sinh(z)}= \frac{e^z + e^{-z}}{e^z - e^{-z}}\\\end{array}$

Complex Inverse Functions.

$\begin{array}{ll} \hline\mbox{\bf Function} & \mbox{\bf Formula} \\ \hline\mbox{Inverse sine} & \sin^{-1}(z) = \frac{1}{j}\ln(jz \pm\sqrt{1-z^2}\\\mbox{Inverse cosine} & \cos^{-1}(z) = \frac{1}{j}\ln(z \pm\sqrt{z^2-1}\\\mbox{Inverse tangent} & \tan^{-1}(z) = \frac{1}{2j} ln(\frac{1 + jz}{1 -jz})\\\mbox{Inverse cotangent} & \cot^{-1}(z) = \frac{1}{2j} ln(\frac{ z + j}{z- j})\\\mbox{Inverse cosecant} & \csc^{-1}(z) = \frac{1}{j}\ln(\frac{j+\sqrt{z^2-1}}{2})\\\mbox{Inverse secant} & \sec^{-1}(z) = \frac{1}{j}\ln(\frac{1+\sqrt{1-z^2}}{2})\\\mbox{Inverse hyperbolic sine} &\sinh^{-1}(z) = \ln(z + \sqrt{z^2+1})\\\mbox{Inverse hyperbolic cosine}&\cosh^{-1}(z) = \ln(z + \sqrt{z^2-1})\\\mbox{Inverse hyperbolic tangent}&\tanh^{-1}(z) = (1/2) ln(\frac{1+z}{1-z})\\\mbox{Inverse hyperbolic cosecant}&csch^{-1}(z) = \ln(\frac{1 + \sqrt{z^2+1}}{2})\\\mbox{Inverse hyperbolic secant}& sech^{-1} (z) = \ln(\frac{1 + \sqrt{1-z^2}}{2}\\\mbox{Inverse hyperbolic cotangent}&\coth^{-}(z)= (1/2) \ln(\frac{z+1}{z-1})\\\end{array}$

Relationships between trig and hyperbolic complex functions.

$\begin{array}{ll}\sin (jz) = j \sinh(z) & \sin(z)= -j \sinh(jz)\\\sinh (jz)= j \sin(z) & \cos(z) = \cosh(jz) \\\cos (jz) = \cosh(z) & \tan(z) = -j \tanh(jz)\\\cosh (jz) = \cos(z) & \sinh(2 + j 2\pi) = \sinh(z) \\\tan (jz) = j \tanh(z) & \sinh(z + j\pi = -\sinh(z) \\\tanh (z) = j \tan(z) & \sinh(z + j\pi/2) = j \cosh(z) \\\cosh (z + j 2\pi) = \cosh(z)&cos(z + j\pi) = -\cosh(z)\\\cosh(z + j\pi/2) = j\sinh(z) \\\end{array}$

Please comment in case of errors! Any errors will be fixed right away!

Posted in Complex Algebra, Complex Numbers | Click for Comments »

repost: Complex Algebra: Basic Operations and Functions of a complex number.

April 24th, 2012

This is a repost of an article which originally appeared in our former Optimal Learning Systems site.

Let $z_1 = x_1 + j y_1= r_1 \angle\theta_1= (x_1, y_1)$ and $z_2 = x_2 + j y_2= r_2 \angle\theta_2= (x_2, y_2)$ .

$\begin{array}{ll}\mbox{Equivalence} & z_1 = z_2 \mbox{ iff } x_1=x_2 \mbox{ and } y_1 = y_2. \\\mbox{Addition} & z_1 + z_2 = (x_1 + x_2) + j( y_1 + y_2)\\\mbox{Subtraction} & z_1 - z_2 = (x_1 - x_2) + j( y_1 - y_2)\\\mbox{Multiplication} &z_1 z_2 = (x_1 x_2 - y_1 y_2) + j(x_1 y2 + x_2 y_1)\\ & = r_1 r_2 \angle (\theta_1 + \theta_2) \\ & = r_1 r_2 [cos(\theta_1 + \theta_2 ) + j sin(\theta_1 + \theta_2)]\\\mbox{Division} & z_1 /z_2 = \frac{x-1 x_2 + y_1 y_2}{x_2^2 + y_2^2} -j\frac{x_2 y_1 - x_1 y_2}{x_2^2 + y_2^2}\\ & = \frac{r_1}{r_2} \angle {(\theta_1 - \theta_2)}\\ & = \frac{r_1}{r_2} [\cos(\theta_1 - \theta_2)+ j \sin(\theta_1 - \theta_2)]\\\mbox{Sum or reciprocals} & \frac{1}{z_1} + \frac{1}{z_2}= \frac{z_1+ z_2}{z_1 z_2}\\ & = \frac{x_1}{x_1^2+ y_1^2}+ \frac{x_2}{x_2^2 + y_2^2} - j [\frac{y_1}{x_1^2 + y_1^2} +\frac{y_2}{x_2^2 + y_2^2}]\\ \mbox{Product of} z_1 & z_1 \overline{z_2} = (x_1 x_2 y_1y_2) - j (x_1 y_2 - y_1 x_2)\\ \mbox{ and conjugate of }z_2 &= r_1 r_2 \angle(\theta_1 - \theta_2) \\\mbox{Dot product} & |z_1||z_2| \cos(\theta) = (x_1 x_2 + y_1 y_2) \\ & = R_e(\overline{z_1} z_2) \\ & =\frac{1}{2} (\overline{z_1} z_2 + z_1 \overline{z_2} \\\mbox{Cross product} & |z_1||z_2| \sin(\theta) = x_1 y_2 - y_1 x_2 \\ & = Im(\overline{z_1} z_2)\\ & = \frac{1}{2j} (\overline{z_1} x_2 + z_1 \overline{z_2})\\\mbox{Principal value of } \ln (z_1 z_2) & \ln(z_1) + \ln(z_2) - i 2\pi; \pi < \theta_1+\theta_2 \le 2 \pi\\ &=\ln (z_1) +\ln z_2 ; -\pi < \theta_1+\theta_2 \le 2 \pi\\ &=\ln (z_1) +\ln(z_2) + j 2\pi ; -2\pi < \theta_1+\theta_2 \le -\pi\\ \end{array}$

$\begin{array}{ll}\mbox{\bf Function} & \mbox{\bf Formula} \\ \mbox{Real part} & Re (z) = x = \frac{1}{2}(z + \overline{z})\\ \mbox{Imaginary part} & Im(z) = y = \frac{1}{2j}( z - \overline{z}\\ \mbox{Absolute value} & mod(z) = |z| = r = \sqrt{x^2 +y^2} = \sqrt{z\overline{z}}\\ \mbox{Norm}& norm(z) = r^2 = x^2 + y^2 = z\overline{z}\\ \mbox{Argument} & arg(z)= \theta = \tan^{-1}(y/x) = \sin^{-1} (y/r)\\ \mbox{or amplitude} &= \cos^{-1} (x/r)\\ \mbox{Conjugate} & \overline{z} = z^* = x- jy = re^{-j\theta} = r cis(-\theta)= (x, -y)\\\mbox{Square} & z^2 = (x^2-y^2) + j xy= r^2 \angle(2\theta)= r^2 [cos(2\theta) + j \sin(2\theta) \\\mbox{Square roots}& \pm \sqrt{z} = \pm(\sqrt{r} (cos(\theta/2) + j \sin(\theta/2)\\ & \pm [\frac{|z|+x}{2}+ sign(y) j \sqrt{\frac{|z|-x}{2}}\\\mbox{Integral power} & z^n = r^n \angle(n\theta) = r^n[\cos(n\theta) + j \sin(n\theta)]\\\mbox{Integral roots} & z^{(1/n)}= r^{(1/n)}[\cos(\frac{\theta + 2k\pi}{n}) + j \sin(\frac{\theta + 2k\pi}{n})]\\ & \mbox{for k }= 0, 1, \ldots, n-1\\\mbox{Rational roots} & z^{(p/q)}= r^{(p/q)}[\cos[(p/q)(\theta + 2k\pi)] + j \sin[(p/q)(\theta + 2k\pi)]]\\ & \mbox{for k }= 0, 1, \ldots, p-1\\\mbox{General power} & z^c = e^{c\ln(z)}, \mbox{many valued unless c is a rational number.}\\\mbox{Exponential } & e^z = e^{(x + jy)} = e^x [\cos(y)+ j\sin(y)]\\\mbox{Reciprocal} & 1/z = \frac{x}{x^2+y^2}- j\frac{y}{x^2+y^2} = (1/r) \angle (-\theta)\\\mbox{Natural log} & \ln(z) = ln(|z|) + j (\theta + 2n\pi), n= 0, \pm 1, \pm 2, \ldots\\\mbox{Principal value } ln(z) & = \ln(|z|) + j\theta \\\mbox{Principal value } ln (z^m) & = m \ln(z) - j 2k\pi, \mbox{k is unique integer satisfying}\\ & \frac{m}{2\pi} arg(z) - 1/2\le k \le \frac{m}{2\pi}arg(z) + 1/2\\\end{array}$

Finally, in the next post for Complex Algebra, we shall list the trigonometric and hyperbolic functions including their inverses for complex numbers.

Posted in Complex Numbers | Click for Comments »

repost: The many ways of specifying a straight line

April 24th, 2012

This is originally from our alternative site Optimal Learning Systems.

Two-point, intercept form

Given two points $(x_1, y_1), (x_2,y_2)$ along the line: $y = \frac{y_2-y_1}{x_2-x_1} x + b$ where $b$ is the intercept, i.e., $(0, b)$ is on the line.

Point slope form

Given the slope $m$ and a point $(x_1, y_1)$ on the line:
$y = y_1 + m (x-x_1)$

Slope intercept form

Given the slope and the point (0, y_1) on the line: $y = m x + y_1$

Intercepts form

Given $(a,0)$ and $(0, b)$ : $\frac{x}{a} +\frac{y}{b} = 1.$

Parametric trigonometric form

Given the angle $\theta$ which the line makes with the positive x-axis, and a fixed point, $(x_1, y_1)$ on the line: $x= x_1 + r\cos(\theta); y = y_1 + r \sin(\theta)$
where r = distance from $(x,y)$ to $(x_1 y_1)$ .

Trigonometric perpindicular distance to origin:
Let p be the perpindicular distance to origin. and $\theta$ angle of line in standard position. Then

$x cos (\theta) + y \sin(\theta) = p$ .
General form

Ax + By = C.

Vector form

Let a be a vector to a point on the line, then any vector from the origin to any other point on the line may be written as: $\bf{r} = \bf{a} + t \bf{b}$ where t is a real number parameter.

Posted in Analytic Geometry | Click for Comments »

reposted: Mean Value Theorems of Calculus.

April 24th, 2012

The original post was in our alternative site, Optimal Learning Systems.org.

Rolle's Theorem

If $f(x)$ is continuous in $[a,b]$ and differentiable in $(a,b)$ , then there exists a point $c \in (a, b)$ such that $f'(c) = 0.$

Theorem of the Mean
If $f(x)$ is continuous in $[a,b]$ and differentiable in $(a,b)$ , then there exists a point $c \in (a, b)$ such that $\frac{f(b)-f(a) }{b-a} = f'(c)$ .
Cauchy's theorem of the mean
If $f(x)$ and $g(x)$ are continuous in $[a,b]$ and differentiable in $(a,b)$ , then there exists a point $c \in (a, b)$ such that

$\frac{f(b)-f(a)}{g(b) - g(a)}= \frac{f'(c)}{g'(c)}$
Taylor's theorem of the mean:
(Future article on Power series expansion of function centered at a point a.)
Mean value theorem for function of two variables:
If f(x,y) is continuous in a closed region and if the first partial derivatives exist in the open region , then

$f(x_0 + h , y_0 + k) - f(x_0, y_0) = h f_x(x_0 + \theta h, y_0 + \theta k) + k f_y (x_0 + \theta h, y_0 + \theta k)$

Posted in calculus | Click for Comments »

Important fluid flow dimensionless groups in engineering.

April 24th, 2012

Originally published in Optimal-Learning-Systems.org(Life, Research, Education on the Web).

These numbers are used in dimensional scaling of models, hydrodynamics and aeronautics.

Reynolds Number, $N_R$ or $R_e$ :
$N_R = \frac{VD\rho}{\mu}$

Viscuous forces are dominant.

$V$ average fluid velocity

$D$ diameter of pipe

$\rho$ fluid density

$\mu$ viscosity
Froude's Number, $N_F$
$N_F = \frac{V^2}{gL}$

Gravitational forces are dominant.

$V$ average fluid velocity

$g$ acceleration due to gravity

$L$ characteristic length
Mach Number, $N_M$ or $M$
$N_M = \frac{V}{\sqrt{\frac{E}{\rho}}}= \frac{V}{a}$

Elasticity forces are dominant.

$V$ average fluid velocity

$E$ modulus of elasticity of fluid

$\rho$ fluid density

$a$ acoustic velocity
Prandtl Number, $N_{Pr}$ or $P_R$
$N_{Pr} = \frac{u c}{\kappa}$

$\mu$ viscosity

$c$ specific heat

$\kappa$ conductivity
Nusselt's number, $N_{Nu}$ or $N_u$
$N_{Nu} = \frac{hL}{\kappa}$

$h$ Heat transfer film coefficient

$L$ characteristic surface length

$\kappa$ conductivity
Weber's number, $N_{W}$
$N_{W} = \frac{V^2L\rho}{\sigma}$

$V$ fluid velocity

$L$ characteristic length

$\rho$ fluid density

$\sigma$ surface tension
Grashoff's number, $N_{Gr}$
$N_{Gr} = \frac{L^3\rho^2\beta g \theta}{\mu^2}$

$L$ surface characteristic length

$\rho$ fluid density

$\beta$ cubical expansion coefficient

$g$ acceleration due to gravity

$\theta$ temperature

$\mu$ viscosity
Graetz number, $N_{Gz}$
$N_{Gz} = \frac{\dot{m} c}{\kappa L}$

$\dot{m}$ mass of fluid flowing per time

$c$ specific heat

$\kappa$ condctivity

$L$ length
Karman number, $N_{K}=N_{K} = \frac{D\rho}{\mu}\sqrt{\frac{2g_c D \overline{L_{wf}}}{L}}$
$N_K= N_R \sqrt{f}$

$gc$ gravitational constant (conversion factor)

$D$ diameter

$\rho$ fluid density

$L$ length

$\overline{L_{wf}}$ friction loss, (in fluid height)
Peclet number, $N_{Pe}$ or $P_e$
$N_{P_e} = \frac{Dv\rho c}{k}= R_e P_r$
Stanton Number, N_{st} or $S_t$
$N_{st}= \frac{h}{V\rho c}=\frac{N_U}{R_e P_r}$
Schmidt NUmber, $S_c$
$S_c = \frac{\mu}{\rho D_G}$

$D_G$ Molecular diffusibility in the gas phase (area /time).

Posted in Uncategorized | Click for Comments »

republished: Formulas for Numerical Differentiation with Error Estimates

April 23rd, 2012

Originally published in http://optimal-learning-systems.org/wp/?p=136

Let $f(x)$ be the function whose first or second derivatives at $x = a$ are desired.

$\begin{array}{|l|l|l|}\hline Method &Formula & Error \\ \hline \mbox{Forward difference} & f'(a) = \frac{f(a+h) - f(a}{h}& \frac{-1}{2} h f^{(2)} (\varphi)\\ \mbox{Central difference} & f'(a)= \frac{f(a + h) - f(a -h)}{2h}& \frac {-h^2}{6} f^{(3)}(\varphi) \\ \mbox{Four point} & f'(a) = \frac{-3 f(a_ + 4 f(a+h) - f(a + 2h)}{2h} & \frac{h^2}{3} f^2(\varphi)\\ \mbox{Five point} & f'(a) = \frac{[f(a -2h) - 8 f(a -h) + 8 f(a +h) - f(a + 2h)]}{12h} & \\ & f''(a)= \frac{f(a) - 2 f(a +h) + f(a +2h}{h^2} & \frac{h^2}{6}f^{iv}(\varphi) - hf''' (\varphi) \\ & f''(a)= \frac{f(a-h) - 2 f(a) + f(a +h)}{h^2} & \frac{-h^2}{12}f^{iv}(\varphi), |\varphi - a | < |a|\\ \hline\end{array}$

Python, Number Theory: generating Pythagorean triples

April 23rd, 2012

Originally published in http://optimal-learning-systems.org/wp/?p=146

Pythagorean triples are a set of three integers forming the sides of a right triangle.
The algorithm to generate these numbers were already known to Euclid, who also
introduced the Euclidean algorithm to determine the greatest common divisor of
two positive integers.

Here is Python code to generate Pythagorean triples.

^?View Code PYTHON

"""
file      pythagtriple.py
author    dr. ernesto p. adorio
          up clarkfield
version   2010.06.26  initial release
"""
 
def gcd(a,b):
    """
    Computes the  greatest common divisor of two integers a and b.
    """
    if a < b: 
       a,b = b, a
    while b != 0:
       a, b = b, a - a//b * b
    return a
 
 
 
def genpytriple(maxa):
    """
    Generates pythagorean triples.
    """
    outlist=[]
    for a in range(2, maxa+1):
       for b in range(1, a):
          if gcd(a,b) == 1:
             x = 2 * a *b 
             y = a * a - b * b
             z = a * a + b * b
             outlist.append((a, b, x,y,z))
    return tuple(outlist)
 
 
outlist = genpytriple(15)
 
print """
<table>
<tr>
<th>i</th><th>a</th><th>b</th><th>x</th><th>y</th><th>z</th></tr>
"""
 
 
for i, (a, b, x, y, z) in enumerate(outlist):
    print "<tr>",
    print "<td>%s</td>" % (i+1),
    print "<td>%s</td>" % a,
    print "<td>%s</td>" % b,
    print "<td>%s</td>" % x,
    print "<td>%s</td>" % y,
    print "<td>%s</td>" % z,
    print "</tr>"
print "</table>"

When the above program is run, it outputs the following html table:

i a b x y z

1 2 1 4 3 5

2 3 1 6 8 10

3 3 2 12 5 13

4 4 1 8 15 17

5 4 3 24 7 25

6 5 1 10 24 26

7 5 2 20 21 29

8 5 3 30 16 34

9 5 4 40 9 41

10 6 1 12 35 37

11 6 5 60 11 61

12 7 1 14 48 50

13 7 2 28 45 53

14 7 3 42 40 58

15 7 4 56 33 65

16 7 5 70 24 74

17 7 6 84 13 85

18 8 1 16 63 65

19 8 3 48 55 73

20 8 5 80 39 89

21 8 7 112 15 113

22 9 1 18 80 82

23 9 2 36 77 85

24 9 4 72 65 97

25 9 5 90 56 106

26 9 7 126 32 130

27 9 8 144 17 145

28 10 1 20 99 101

29 10 3 60 91 109

30 10 7 140 51 149

31 10 9 180 19 181

32 11 1 22 120 122

33 11 2 44 117 125

34 11 3 66 112 130

35 11 4 88 105 137

36 11 5 110 96 146

37 11 6 132 85 157

38 11 7 154 72 170

39 11 8 176 57 185

40 11 9 198 40 202

41 11 10 220 21 221

42 12 1 24 143 145

43 12 5 120 119 169

44 12 7 168 95 193

45 12 11 264 23 265

46 13 1 26 168 170

47 13 2 52 165 173

48 13 3 78 160 178

49 13 4 104 153 185

50 13 5 130 144 194

51 13 6 156 133 205

52 13 7 182 120 218

53 13 8 208 105 233

54 13 9 234 88 250

55 13 10 260 69 269

56 13 11 286 48 290

57 13 12 312 25 313

58 14 1 28 195 197

59 14 3 84 187 205

60 14 5 140 171 221

61 14 9 252 115 277

62 14 11 308 75 317

63 14 13 364 27 365

64 15 1 30 224 226

65 15 2 60 221 229

66 15 4 120 209 241

67 15 7 210 176 274

68 15 8 240 161 289

69 15 11 330 104 346

70 15 13 390 56 394

71 15 14 420 29 421

i	a	b	x	y	z
1	2	1	4	3	5
2	3	1	6	8	10
3	3	2	12	5	13
4	4	1	8	15	17
5	4	3	24	7	25
6	5	1	10	24	26
7	5	2	20	21	29
8	5	3	30	16	34
9	5	4	40	9	41
10	6	1	12	35	37
11	6	5	60	11	61
12	7	1	14	48	50
13	7	2	28	45	53
14	7	3	42	40	58
15	7	4	56	33	65
16	7	5	70	24	74
17	7	6	84	13	85
18	8	1	16	63	65
19	8	3	48	55	73
20	8	5	80	39	89
21	8	7	112	15	113
22	9	1	18	80	82
23	9	2	36	77	85
24	9	4	72	65	97
25	9	5	90	56	106
26	9	7	126	32	130
27	9	8	144	17	145
28	10	1	20	99	101
29	10	3	60	91	109
30	10	7	140	51	149
31	10	9	180	19	181
32	11	1	22	120	122
33	11	2	44	117	125
34	11	3	66	112	130
35	11	4	88	105	137
36	11	5	110	96	146
37	11	6	132	85	157
38	11	7	154	72	170
39	11	8	176	57	185
40	11	9	198	40	202
41	11	10	220	21	221
42	12	1	24	143	145
43	12	5	120	119	169
44	12	7	168	95	193
45	12	11	264	23	265
46	13	1	26	168	170
47	13	2	52	165	173
48	13	3	78	160	178
49	13	4	104	153	185
50	13	5	130	144	194
51	13	6	156	133	205
52	13	7	182	120	218
53	13	8	208	105	233
54	13	9	234	88	250
55	13	10	260	69	269
56	13	11	286	48	290
57	13	12	312	25	313
58	14	1	28	195	197
59	14	3	84	187	205
60	14	5	140	171	221
61	14	9	252	115	277
62	14	11	308	75	317
63	14	13	364	27	365
64	15	1	30	224	226
65	15	2	60	221	229
66	15	4	120	209	241
67	15	7	210	176	274
68	15	8	240	161	289
69	15	11	330	104	346
70	15	13	390	56	394
71	15	14	420	29	421

The first two triples are our familiar 3,4,5 (known to the ancient Egyptians) and 6,8, 10.

Posted in Number Theory | Click for Comments »

republished: Formulas for Area of Triangle.

April 23rd, 2012

Formerly published in http://optimal-learning-systems.org/wp/?p=151.

We present various formulas for computing areas of a tringle.

Base and height (b,h) known: $A = \frac{1}{2}b h$
Three sides (a,b,c) known(Heron's formula): $A = \sqrt{s(s-a)(s-b)(s-c)}= \frac{1}{4}\sqrt{(a + b+ c)(a + b - c) (a-b + c) (-a + b+ c)}$ where
$s = \frac{a + b + c}{2}$
Two adjacent sides and included angle known:
$A = \frac{bc \sin(\alpha)}{2} = \frac{ab sin\gamma}{2}= \frac{ac \sin(\beta}{2}$
One side, three angles known:
$A = a^2 \frac{\sin(\beta) \sin(\gamma)}{2\sin(\alpha)}=b^2 \frac{\sin(\alpha)\sin(\gamma) }{2\sin(\beta)}=c^2 \frac{sin(\alpha)\sin(\beta)}{2\sin(\gamma)}$
Radius of circumscribed circle $R$ , with three sides $(a,b,c)$ known: $A = \frac{abc}{R^2}$
Radius of inscribed circle, $r$ , and $s$ known: $A = rs$
Radius of escribed circle $r_a$ and side $a$ known: $A = r_a (s -a)$ .
Coordinates of vertices $(x_1, y_1), x_2, y_2), (x_3, y_3)$ known:
$A = \frac{1}{2}\left| \begin{array}{lll} 1 & 1 & 1\\ x_1 &x_2 &x_3\\ y_1 & y_2 & y_3\\ \end{array}\right|$

Posted in Mensuration | Click for Comments »

republished: A MultiVariate Function (mvf) library in C

April 23rd, 2012

I am planning to close down my other blogs hosted in another site. I will be transferring some of the articles originally posted there to this blog.

This article was firs published in http://optimal-learning-systems.org/wp/?p=484

When I was still in Diliman, I wrote on my own free time, and without any funding, a library in C consisting of the well known global optimization functions we keep encountering in the optimization literature. I put it up at Geocities. Unfortunately, Geocities was bought by Yahoo but sometime later, Geocities was sent to oblivion. I still remember when searching using Google, the best references were in Geocities! or Angelfire or Tripod.com.

The list of functions included in the library included the Ackley,Branin, Camel, Hartmann,GoldsteinPrice and of course, the famous Rosenbrock function.

I am bringing back from obscurity my mvf work. Readers who wish to view the contents as an html should click on mvf.html and those who prefer a pdf file, should click on mvf.pdf and the source code is available as a C file and the header file is at mvf.h. All files including the latex source files can be obtained by downloading the bzipped file jan.19.mvf.tar.bz2

We will spend more time trying to resuscitate our love of the subject of global optimization, ignoring stupid critics who love disparaging our work and naively thinking that creative scientific programming is a clerical activity!

Googling mvf.c returned the following citations:

1. "The Bees Algorithm: modelling foraging behaviour to solve continuous optimization problems", D T Pham, M Castellani Reference site: http://journals.pepublishing.com/content/t70214132l32p0j0/
Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science

Publisher Professional Engineering Publishing
ISSN 0954-4062 (Print) 2041-2983 (Online)
Issue Volume 223, Number 12 / 2009
DOI 10.1243/09544062JMES1494
Pages 2919-2938

The references cited the following:

E. P. Adorio, 'MVF – multivariate test functions library in C for unconstrained global optimization' (2005): available from http://geocities.com/eadorio/mvf.pdf

2. "Differential Evolution: Fundamentals and Applications in Electrical Engineering", Anyong Qing, 2009, Wiley
Web reference: Qing

3. 'Multidimensional sequential sampling for NURBs-based metamodel development', Engineering with Computers, Vol 23, No.3, Sep. 2007, ISSN 01777-0667(print), 1435- 5663(online)"
Turner(Plutonium manufacturing and technology division, Los Alamos
National Laboratory), Crawford and Campbell(University of Texas at Austin),

Unfortunate that one has to shell out money to view the articles! We hope to be more productive always in spite of the lack of facilities.

Posted in Global Optimization, Multivariate Functions | Click for Comments »

Beware: Prudential Life scam

April 21st, 2012

Frm: PHILIPPINE PRUDENTIAL FINAL NOTIFICATION:

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[044-8158958]
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Received:
03:10:03pm
20-04-2012
Sender:
(noname)
+639234999944

Posted in Scams, Spam | Click for Comments »

Digital explorations

Just another WordPress weblog

It is that time of the year to upgrade the Ubuntu operating system-11.10-Oneiric Ocelot to 12.04-Precise Pangolin

Humor in the classroom. Getting fried by an excuse.

Avoid clicking on links to Facebook Games

The Lyric mobile spam and scam

"A scam in the name of the United Nations Human Settlements Programme" Redux

repost: Complex trigonometric and hyperbolic functions

Complex Trigonometic Functions

Complex Hyperbolic Functions.

Complex Inverse Functions.

Relationships between trig and hyperbolic complex functions.

repost: Complex Algebra: Basic Operations and Functions of a complex number.

repost: The many ways of specifying a straight line

reposted: Mean Value Theorems of Calculus.

Important fluid flow dimensionless groups in engineering.

republished: Formulas for Numerical Differentiation with Error Estimates

Python, Number Theory: generating Pythagorean triples

republished: Formulas for Area of Triangle.

republished: A MultiVariate Function (mvf) library in C

Beware: Prudential Life scam

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