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#1 Re: Help Me ! » Does 1 = .999...? » 2018-08-24 20:41:28

I had a long dispute with a major in mathematics.

So far I can tell you that mathematicians made a cunning update to cover this bug as far as redefining numbers.

#2 Dark Discussions at Cafe Infinity » Laptop with good keyboard is hard to find » 2018-08-24 20:39:55

George,Y
Replies: 0

So far the Thinkpad series is still the best in 14-inch business arena.

The 15.6-inch game laptop has seen some great mechanic keyboard, but it is too large.

Alternative brand Hasee has really great keyboard, but the overall quality of hardware and cooling is rumored unstable.

I hate Apple, because it makes the trend of making keyboard thinner and thinner, worse and worse for typing.

And other followers are foolish to oversee the value of a comfortable, tall keyboard.

#4 Re: Computer Math » Calculating Pi » 2018-08-04 15:25:08

Amartyanil wrote:
George,Y wrote:

If both of them succeeded,  the mistake is located in main

I do not get your point, can you please explain it?

The program now needs an input "accuracy" to start running.

I suggest to cancel this input first and set an accuracy inside the code.

Compile and test it.

#5 Re: Help Me ! » A line is neither concave up nor concave down. what is that line » 2018-08-04 15:21:52

a straight line would satisfy these criteria

if concavity = second derivative of the single variable function

#6 Dark Discussions at Cafe Infinity » React OS will take over Windows as the dominant PC Operating System? » 2018-07-30 23:18:50

George,Y
Replies: 3

https://www.youtube.com/watch?v=Ne88Is2cymQ

A nice copy of Windows,

but open source and supported by community

#8 Re: Dark Discussions at Cafe Infinity » Martial Arts are completely useless » 2018-07-29 00:33:07

Be aware of some specialized "martial arts" which prohibits some attacks at its weak sides.  Taekwondo, prohibits throwing, for example. Judo prohibits punching and kicking.

These can be called fake martial arts because they don't stand the chance if an opponent attacks at the weak sides using the usually banned strike.

A very rounded martial arts at least declares how to combat other main styles of fighting.

You can try some Chinese style and ask if they have this content.

Taiji, for example, is another fake martial arts.

Shaolin fight technique, is not.

#9 Re: Coder's Corner » Python: moving on up? » 2018-07-29 00:26:24

PyQt is also a good choice.

Anyone still here?

#10 Re: This is Cool » Why prime numbers aren't random » 2018-07-24 01:13:58

random is an excuse for unable to find the true cause.

#11 Re: Computer Math » How a computer sees it. » 2018-07-24 01:11:03

ericnumberking wrote:
bobbym wrote:

I may have been a bit hasty when I wrote that. I meant to say a lot better.

And the truth shall set you free . . . good one!

He has passed away.

sad

#12 Re: Computer Math » Calculating Pi » 2018-07-24 01:09:45

I suggest you test if the problem is a pure IO one.

Just change the code to compulsively calculate the function on a certain accuracy you put in the code.

And compile it to see if it runs properly.

Then alter the code with another value of accuracy, and test again.

If both of them succeeded,  the mistake is located in main

#13 Re: Help Me ! » Probability question to do with a tennis match » 2018-05-27 14:18:15

It is a really great question!

The binomial tree bob uses is a common tool in stochastic calculus and the problem that you posted is similar to gambler's ruin problem.

The gambler's ruin problem is like this. A gambler has n coins and went to gamble. A win gets another coin and a lose gives away one. How long does it take for him to lose all coins?

It is also named as barrier problem.

The question you posted is more complicated -  a double barrier instead of one barrier. A has to win before B wins.

I remember such problem usually involves alternative probability series to cancel out over-counting.

#14 Science HQ » Combustion physics » 2018-05-21 15:15:29

George,Y
Replies: 0

The flame is not gas, not fluid, not solid, but moving plasma.

However the speed and direction of the plasma is highly influenced by that of reactant and environment.

Examples include ejecting flame, chimney effect and dancing flame in the wind.

It is commonly neglected that the plasma itself prohibits gas diffusion.

So sometimes the combustion is incomplete - the fresh air cannot freely get into the flame and react with the fuel.

And as a flame is loaded above -  a pot on flame. e.g.

this plasma barrier gets stronger, and a complete combustion could turn incomplete.

A flame on candle may not produce black smoke (a sign of incomplete combustion), but will leave black stain at the bottom of some solid above it.

I invented the idea of plasma barrier, or has it already been found? smile

#15 Re: Science HQ » electrostatics... » 2018-05-21 14:51:56

Mathegocart wrote:

yikes it's George Y!

Hey, long time not seeing you guys!

#16 Re: Science HQ » electrostatics... » 2018-05-21 14:50:45

iamaditya wrote:

Hi George, Y.

Were you there all the time? Why did you not post anything...

Sorry guys, I went through a chaos of changing and losing jobs.

I was not in the mood for mathematics.

#17 Re: Science HQ » electrostatics... » 2018-02-25 02:19:10

Otherwise the electrons will flow from areas with lower potential to that with higher potential

#18 Re: This is Cool » the Mythical formula to calculate Numerical Derivatives! » 2018-02-12 22:42:05

zetafunc wrote:

These coefficients are part of a more general phenomenon called the Savitzky-Golay filter in numerical analysis. In fact the traditional five-point 'stencil' reads:

where
. You can derive this result simply by playing around with the Taylor series for
with
. It's a little tedious, but you can see the derivation here: https://en.wikipedia.org/wiki/Five-poin … he_formula

There are analogous formulae for higher order derivatives too, and several published papers about the error term.

That is very informative, zeta. Thanks for the reply.

I wonder if there is a way to calculate the midpoint differentials by 4 points around it:

dy/dx ]x=0

ddy/dx/dx ]x=0

given y[-0.5], y[0.5], y[-1.5] & y[1.5]

#19 This is Cool » the Mythical formula to calculate Numerical Derivatives! » 2018-02-11 20:48:31

George,Y
Replies: 2

I come across this method when trying to calculate the derivative of an unknown curve which I have only sample points at equal grids.

The simplest way to calculate numerical derivative is three-point formula:

dy/dx = (y[1]-y[-1]) /2/dx
ddy/dx/dx = (y[1]+y[-1]-2*y[0]) /dx/dx

But I found this one on five points :

dy/dx = ( y[-2] -8*y[-1] +8*y[1] -y[2]) / (12*dx)

ddy/dx/dx = (-y[-2] +16*y[-1] -30*y[0]+ 16*y[1] -y[2])  / (12*dx^2)

It is surprisingly accurate when I test the derivative on exp(3) using exp(2) exp(2.5) exp(3) exp(3.5) exp(4)

the result of 1st numerical derivative and 2nd are
20.04243  &   20.07127

remember the correct answer are both exp(3) = 20.08554

Can anyone prove how this works?
4th polynomial?

#21 Re: Help Me ! » Need help with building a Curriculum » 2018-01-13 23:01:02

I suggest you read books one by one.
Today's textbooks are very concise, and you can learn most topics up to undergraduate level on your own

#22 Re: Help Me ! » Arithmetic and Geometric Sequences » 2018-01-13 22:58:26

Note the common ratio is a complex number.

#23 Re: Dark Discussions at Cafe Infinity » Breathing Trouble while Meditation » 2018-01-13 22:55:58

Uh it is surprising to find so many mathematicians practice meditation!

#25 Re: Help Me ! » Matrix inverse proof » 2017-12-25 01:57:29

AX =  X diag( 入i )

V := X^(-1)

AX diag( 1/ 入i )V  =  X diag( 入i )diag( 1/ 入i ) V  = I

thus


A^(-1) =  X diag( 1/ 入i ) X^(-1)

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