Math
Integer solutions of pythagorean triangle relation
1 4 9 16 25 36 49 …. 1 3 5 7 9 11 13 Read more…
Genetics
Video: Ultraconservation and living fossils Mysteries of the Human Genome
Genetic code is reused in exactly the same manner human programmers reuse code. Thus once some random string of genetic coding is found useful there is a process that preserves it from change. That change is called survival. If it is a random string with no purpose then it is Read more…
Information-Theory
Quantum Entanglement of Photons demonstrated in relatively low cost set up
Louis DeBroglie does not get the credit he deserves for original thinking in quantum machanics – DeBroglie thesis paper – he won the Nobel Prize in 1929 for very good reasons which you will see if you read his thesis paper. I am looking for the single photon counter used Read more…
Computing
Memristor based nano computing promises to revolutionalize the ways we compute
When memory elements become nonvolatile and can be configured as processing elements computing is going to start to use very different approaches. Behavoiral evolution approaches will become dominant. Professor Chua talks with a more mathematical presentation on the memristor.
Math
Find the equilateral triangle
Show that the curve: contains only one set of three distinct points, A, B, and C, which are vertices of an equilateral triangle, and find its area. The “curve” is actually reducible, because the left side factors as Moreover, the second factor is so it only vanishes at . Read more…
Math
Long hand division generation of polynomials
Do a long hand division of x greater than or equal to 1 does not result in convergence of this sum. However this algorithm can still be used to do some interesting things. Let us use a complex value of Each power of x yields a result one step around Read more…
Math
Z transform of and exponentially decaying sequence
The series: this converges for x < 1 : Both of these expressions are the Z transform of the exponential decay sequence. The first expression is easier to deal with because it is smaller and easier to work with. The following diagram uses a decay sequence with The filter Read more…
Linear-System-Theory
Convolution of time signals using polynomials-The Super Easy Z transform
The filter is the sum of the last 3 signal samples. The signal is a pulse set of three ones. The signal arrives 1 sample at a time. Notice the coefficients of the multiplied polynomials are equal to the signal output values at times 0 through 4. If Read more…
Math
Two 2 dimensional determinant of a matrix animation showing it is equal to the area of the parallelogram
The 2 dimensional determinant of a matrix can be interpreted as the area of a parallelogram as shown in the following diagram. Numeric Example Compare that with the old fashioned area of two triangles that make up the parallelogram: Using Pythagoras: This carries on through higher dimensions. Read more…