Chromatography: a glance from XXI century

Written by Aram Hayrapetyan

Dear Colleague!


I am sure it interests You - especially in attaining a maximum efficiency ofrepparttar chromatographic column in use. It should be acknowledged that not all has been done yet in this field of chromatography. That's whyrepparttar 127664 proposed technology has a high significance. Thus a new basis has been opened from whichrepparttar 127665 whole philosophy ofrepparttar 127666 theory of Chromabarography can be easily developed as an entity, and I suppose inrepparttar 127667 near future we shall have experimentally confirmed such a theory of chromatography which will evidently be similar to geometry.

I hope I managed You to get acquainted withrepparttar 127668 advantages ofrepparttar 127669 new basic technology of chromatography - Chromabarography (Hayrapetyan's Effect). It is interesting, do you not think so?

It follows to note thatrepparttar 127670 virtually presented information about chromabarography opens onlyrepparttar 127671 top ofrepparttar 127672 iceberg. I think you will evaluate and determine yourselfrepparttar 127673 diagnosis ofrepparttar 127674 contemporary state ofrepparttar 127675 competitiveness ofrepparttar 127676 chromatographic apparatus and ofrepparttar 127677 technologies applied and will get measured answers forrepparttar 127678 main questions:

Nature Will Not Imagine

Written by Charles Douglas Wehner

Mathematicians can be pig-headed. Sometimes there are problems that admit of no solution, butrepparttar mathematician ignores common sense and presses on regardless.


Pythagoras gave an answer. The hypotenuse is a unit, so you square it. The square is still a unit. Now you look atrepparttar 127663 position torepparttar 127664 right. It is five units. You square it to twenty-five and take it away.

Then you findrepparttar 127665 square root.

But one minus twenty-five is MINUS TWENTY-FOUR. What isrepparttar 127666 root of a negative number?

There is no answer!

But common sense tells you that nothing can be on a circle if it is further fromrepparttar 127667 centre thanrepparttar 127668 radius. The answer "NOT ON THE CIRCLE" leaps to mind.

Girolamo Cardano was a mathematician who was even consulted by Leonardo da Vinci. He was also a gambler, but used his knowledge of probability to getrepparttar 127669 better of his opponents. He decided that he hadrepparttar 127670 solution.

You split uprepparttar 127671 problem into two parts. The root of 36 is 6. However, one can tryrepparttar 127672 root of 4 times 9 - in which case one hasrepparttar 127673 root of 4 timesrepparttar 127674 root of 9. The answer isrepparttar 127675 same.

So you look forrepparttar 127676 root of -1 timesrepparttar 127677 root of 24.

The root of any negative number will berepparttar 127678 root of -1 timesrepparttar 127679 root ofrepparttar 127680 absolute value of that number.

Sorepparttar 127681 root of -36 isrepparttar 127682 root of -1 times six.

The root of -1 is defined as IMAGINARY, sorepparttar 127683 root of -36 is IMAGINARY SIX. Andrepparttar 127684 answer torepparttar 127685 position on a unit circle ofrepparttar 127686 point X=5? That will be Y=IMAGINARY ROOT 24.

Cardano was scoffed at. He died. The years went by, and slowlyrepparttar 127687 mathematical community began to realise thatrepparttar 127688 idea was not quite so bad after all.

It was a NEW TECHNIQUE. To solve problems, you simply followrepparttar 127689 rules slavishly. These rules began to be taught inrepparttar 127690 universities. People were taught thatrepparttar 127691 old numbers -repparttar 127692 REAL ones - had to be kept separate fromrepparttar 127693 imaginary ones. They learned to describe a two-part number having real and imaginary as a COMPLEX NUMBER.

The rules say that whenever you multiply real by real you get real. Multiply real by imaginary (of imaginary by real) and you get imaginary. Multiply imaginary by imaginary and you get MINUS real.

Simple rules, easy to apply.

But how does this impact uponrepparttar 127694 whole of mathematics? What happens to sines, cosines, logarithms and other things when you use complex numbers in place of real ones? A host of great mathematicians - includingrepparttar 127695 legendary Leonhard Euler - worked on this question. Complex mathematics was becoming established as a standard tool.

Problems began to become apparent. The simplistic concept of ROOT -1 was actually wrong. It should have been "ONE OF THE ROOTS OF -1". There are actually two.

Thenrepparttar 127696 problem of multiple solutions appeared. As I wrote at , this problem can be visualised by consideringrepparttar 127697 antilogarithm of an imaginary number as a SPIRAL IN COMPLEX SPACE. What isrepparttar 127698 lowest point? One for every turn ofrepparttar 127699 spiral. Therefore multiple solutions.

I then continuedrepparttar 127700 research by delving deeply into Euler's GAMMA FUNCTION. Here, for numbers below zero,repparttar 127701 result negates in unit steps. I called thisrepparttar 127702 NEGATION FUNCTION, which is also a spiral in complex space.

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