Chromatography: a glance from XXI century

Written by Aram Hayrapetyan

Continued from page 1

Where are You? Where arerepparttar others?! What do they offer and where to move from here? ... ... and on this basis will make a choice ofrepparttar 127664 purposes of competitive strategy: Your firm's development, preservation of its goodwill; organizations of researches forrepparttar 127665 creation and manufacture of more modern means of analytical instrument-making withrepparttar 127666 use ofrepparttar 127667 basic technology - Chromabarography;

development of original, high-effective methods of chromatographic analysis, etc. And in this is concluded my aim!

So,repparttar 127668 choice is Yours ...

With best regards, Aram Hayrapetyan

ARAM HAYRAPETYAN Born 17 May 1945, married, two children. Daughter born 1972, married. Son born 1977. 47/6 Vardanants Street, Vanadzor 377201, Republic of Armenia, E-mail: Web-site: HTTP://CHROMATOGRAPHY.HOTBOX.RU

Nature Will Not Imagine

Written by Charles Douglas Wehner

Continued from page 1

I posedrepparttar riddle, how do you create a diagram ofrepparttar 127663 Gamma function when it spirals in one place and not inrepparttar 127664 other?

I solved that riddle with a surprising answer. NATURE IN THIS CONTEXT REJECTS THE IMAGINARY. There is no solution torepparttar 127665 Gamma Function if you use complex maths. There is no complex space.

That is to say,repparttar 127666 square root of -1 has two answers, but Nature insists that you must take them BOTH AT THE SAME TIME.

This is quite different torepparttar 127667 roots of real numbers. The roots of 4 are 2 *OR* -2.

The roots of -1 are i1 *AND* -i1. Take BOTH or NONE, inrepparttar 127668 case ofrepparttar 127669 Gamma Function. Otherwise,repparttar 127670 riddle is insoluble.

But i1 makesrepparttar 127671 spiral go left whilst -i1 makesrepparttar 127672 spiral go right. Makingrepparttar 127673 spiral go equally left and right will STOP it from spiralling. So both isrepparttar 127674 equivalent of none. Nature has REJECTEDrepparttar 127675 imaginary.

At this point I wrote ( ) that "If it can be shown for other functions unrelated torepparttar 127676 Gamma function, and having a negation function, that Nature rejectsrepparttar 127677 imaginary axis in this way, then it can be said that Nature rejects complex mathematics as a human product. "

I had not expected that Nature would then reveal to me a function that rejectsrepparttar 127678 imaginary axis without having a negation function. It isrepparttar 127679 INVERSE function torepparttar 127680 exponential. That is to say, it isrepparttar 127681 LOGARITHM.

Fromrepparttar 127682 first page above, you can visualise Euler's equation forrepparttar 127683 exponential (exp(i X) = cos(X) + i sin(X)) as a spiral. You can see that exp(i Pi) gives -1. So does exp (i 3Pi). So does exp (i 5Pi). So do ALLrepparttar 127684 odd imaginary multiples of Pi. So do allrepparttar 127685 negative values of those odd imaginary multiples.

Sorepparttar 127686 log of -1 is ALL of those positive and negative odd imaginary multiples of Pi. It does not really matter whether they are AND or OR. It only matters that they are there.

I then consideredrepparttar 127687 logarithm of zero. This is known to be MINUS INFINITY.

But what of MINUS ZERO? This may seem like a silly question, but it is not. We have consideredrepparttar 127688 log of any negative number to berepparttar 127689 log ofrepparttar 127690 positive equivalent plus one or more odd imaginary multiples of Pi. Sorepparttar 127691 log of minus zero will be minus infinity just likerepparttar 127692 log of zero - but with a DIFFERENCE.

For allrepparttar 127693 negative numbers,repparttar 127694 logarithm is as forrepparttar 127695 positive but TOGETHER WITH THE SERRIED RANKS OF ODD IMAGINARY PIs. Asrepparttar 127696 numbers rise, they get closer and closer towards zero, andrepparttar 127697 real part ofrepparttar 127698 logarithm goes downwards towards minus infinity.

Then they hit zero. Those serried ranks of imaginary numbers STOP. That's it! They VANISH.

One would call this a SINGULARITY, but it is more than that. There are INFINITE odd imaginary multiples of Pi, and they ALL stop together atrepparttar 127699 point X=0.

So Nature again is REFUSINGrepparttar 127700 imaginary.

Natural laws tend to flow smoothly throughoutrepparttar 127701 number continuum. For an entire family of numbers - all odd imaginary multiples of Pi - and therefore by inference a whole SET -repparttar 127702 set of all imaginary - to stop is quite unnatural.

Sorepparttar 127703 imaginary numbers arerepparttar 127704 imaginings of Humankind. Nature does not imagine.

Charles Douglas Wehner

Born in 1944, Charles Wehner is an electronics engineer, technical author and former factory manager.

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