Subject: Vietmath War: ...002 bootcamp for p-adics
From: Archimedes.Plutonium@dartmouth.edu (Archimedes Plutonium)
Date: 13 Nov 1996 20:58:42 GMT
Newsgroups: sci.math
From: Ludwig.Plutonium@dartmouth.edu (Ludwig Plutonium)
Subject: Re: FermatÕs Last Theorem
Message-ID:
Organization: Dartmouth College, Hanover, NH
References: <2728f8$51j@news.u.washington.edu>
<278vgj$pi2@paperboy.osf.org>
Date: Fri, 17 Sep 1993 03:19:22 GMT
Lines: 44
In article
Ludwig.Plutonium@dartmouth.edu (Ludwig Plutonium)
>In article <278vgj$pi2@paperboy.osf.org> karl@dme3.osf.org (Karl
>Heuer) writes:
>
>>Ludwig.Plutonium@dartmouth.edu (Ludwig Plutonium) writes:
>>>The eventual arithmetic proof of FLT, I am confident, will come
>>>from the counting numbers; P-triples are possible only in exp2
>>>because 2+2=2x2=4.
>>
>>I have my doubts as to the connection between that equation and
>>FLT; however, you may be interested to know that other solutions
>>are possible if you allow those left-infinite decimal strings that
>>we discussed earlier. When k=4, there is a unique nonzero solution
>>to N+N+N+N = N*N*N*N = M. Here is the answer, worked out to 60
>>decimal places. You can check it by doing the arithmetic yourself,
>>right to left.
>>
>> N = . . .8217568575974462578891103859665245689398767183
>> 82655349981184
>> M = . . .2870274303897850315564415438660982757595068735
>> 30621399924736
>>
>>Karl Heuer karl@osf.org
>
> Karl Heuer double bless you to the infinite Fields of Elysium. I >would not mind if you discovered the worldÕs first valid proof of >FLT, instead of me.
> Karl can you do the same thing for exp3 and exp5, i.e., a unique >solution?
Karl I think the proof would then go like this. Take any exp
greater than 2, then when there are rational solutions to FLT those are
turned into infinite integers by just deleting the decimal point. Near
the end of the proof would be something that only with finite integers
is a Ptriple possible because only 2+2=2x2=4.
Then again I could be all wrong and there in fact exists a
counterexample to FLT provided that one considers infinite integers are
no different from finite integers. That is, finite integers are
infinite integers with just infinite repetition of zeroes to the left.
WOULD THAT NOT BE THE SUPREME IRONY SO FAR IN THE HISTORY OF MATH. That
there is a counterexample to FLT. The whole world will laugh
hysterically if Wiles gets approval and Ludwig Plutonium comes up with
the counterexample. Which choice would you pick--- a 1000 page math
community accepted (fake) proof, or a counterexample? So far my
confidence in the math community is that they would prefer the 1000
page ordeal.
-------------------------------------------------------------
Newsgroups: sci.math
From: Ludwig.Plutonium@dartmouth.edu (Ludwig Plutonium)
Subject: Re: FermatÕs Last Theorem
Message-ID:
Organization: Dartmouth College, Hanover, NH
References: <2728f8$51j@news.u.washington.edu>
<278vgj$pi2@paperboy.osf.org>
Date: Fri, 17 Sep 1993 03:44:56 GMT
Lines: 9
In article <278vgj$pi2@paperboy.osf.org> karl@dme3.osf.org (Karl Heuer)
writes:
>
> N = . . .8217568575974462578891103859665245689398767183
> 82655349981184
> M = . . .2870274303897850315564415438660982757595068735
> 30621399924736
LET US FIND A CROP OF COUNTEREXAMPLES TO FLT.
Ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha ha!
-------------------------------------------------------------
EMAIL
From: ÒTerry TaoÓ
Date: Sat, 18 Sep 93 09:55:36 EDT
To: Ludwig.Plutonium@Dartmouth.EDU
Subject: Re: FermatÕs Last Theorem
Newsgroups: sci.math
In-Reply-To:
References: <2728f8$51j@news.u.washington.edu>
<278vgj$pi2@paperboy.osf.org>
Organization: Princeton University
Cc:
In article you write:
>In article
>Ludwig.Plutonium@dartmouth.edu (Ludwig Plutonium)
>
>>In article <278vgj$pi2@paperboy.osf.org> karl@dme3.osf.org (Karl
>>Heuer) writes:
>>
>>>Ludwig.Plutonium@dartmouth.edu (Ludwig Plutonium) writes:
>>>>The eventual arithmetic proof of FLT, I am confident, will come
>>>>from the counting numbers; P-triples are possible only in exp2
>>>>because 2+2=2x2=4.
>>>
>>>I have my doubts as to the connection between that equation and
>>>FLT; however, you may be interested to know that other solutions
>>>are possible if you allow those left-infinite decimal strings that
>>>we discussed earlier. When k=4, there is a unique nonzero solution
>>>to N+N+N+N = N*N*N*N = M. Here is the answer, worked out to 60
>>>decimal places. You can check it by doing the arithmetic yourself,
>>>right to left.
>>>
>>> N = . . .8217568575974462578891103859665245689398767183
>>> 82655349981184
>>> M = . . .2870274303897850315564415438660982757595068735
>>> 30621399924736
>>>
>>>Karl Heuer karl@osf.org
>>
>> Karl Heuer double bless you to the infinite Fields of Elysium. I
>>would not mind if you discovered the worldÕs first valid proof of
>>FLT, instead of me.
>> Karl can you do the same thing for exp3 and exp5, i.e., a unique
>>solution?
No.
Theorem. The equation N+N+N=N*N*N has no solution in 10-adics, apart
from N=0.
Proof: consider the powers of 2 and 5 in N. Suppose 2 divides N a times
and 5 divides N b times. The lhs of the above equation has 2^a 5^b as
its factors of 2 and 5 (which are by the way the only primes in
10-adics), and the rhs has 2^3a 5^3b as its factors, hence a and b must
be 0.
But then, if neither 2 or 5 divides N, then N must be invertible,
unless N=0. Thus, dividing by N, we get N*N = 3. But comparing the
final digits of both sides, we see that this is impossible.
Similarly: The equation N+N+N+N+N=N*N*N*N*N has no solution in
10-adics, apart from N=0.
Proof. Suppose 2^a5^b are the prime factors of N, again. Then the lhs
has prime factors of 2^a 5^(b+1) and the rhs has prime factors of 2^5a
5^5b. But these can never match, hence there is no solution (unless
N=0; 0 is the only number that has non-unique prime factorization).
The fact that N+N+N=N*N*N has no solutions in 10-adics, whereas there
ARE solutions of FLT in 10-adics for n=3 (see for example the post by
William Schneeberger), shows that there is no proof that ÒFLT is true
for n=3 => N+N+N=N*N*N for some non-zero NÓ unless you use a property
of the integers that the 10-adic integers do not have.
>
> Karl I think the proof would then go like this. Take any exp
>greater than 2, then when there are rational solutions to FLT those
>are turned into infinite integers by just deleting the decimal point.
An important point here: the operation of turning rational numbers into
infinite integers by deleting the decimal point does NOT preserve
addition or multiplication. For example, in rationals
.33333... x .33333.... = .11111....
whereas
....33333 x ....33333 = .....88889
and
.5555.... + .4444... = 1
whereas
....5555 + ....4444 = ....9999
Thus, a rational solution of FLT does not automatically lead to a
10-adic solution of FLT.
>Near the end of the proof would be something that only with finite
>integers is a Ptriple possible because only 2+2=2x2=4.
I would very much like to see a proof of this statement: if you can
prove this, then you have proved FLT. Then again, see an above point
that you would need to use a property of the integers that is not
shared by the 10-adic integers.
> Then again I could be all wrong and there in fact exists a
>counterexample to FLT provided that one considers infinite integers
>are no different from finite integers.
What you mean here is that there exists a counterexample to FLT in
infinite integers. It is not quite correct to say that Òinfinite
integers are no different from finite integersÓ. Every finite integer
is a 10-adic integer, but not conversely. What is true is that
multiplication and addition are the same operation for both of them.
However, finite integers have several properties that 10-adic integers
do not have, for example, they are all finite. Another is that
induction works for finite integers, but not for 10-adic integers.
(otherwise, you could prove that all 10-adic integers were finite by
induction).
> That is, finite integers are infinite integers with just infinite
>repetition of zeroes to the left. WOULD THAT NOT BE THE SUPREME
>IRONY SO FAR IN THE HISTORY OF MATH. That there is a
>counterexample to FLT.
The commonly accepted wording of FLT ends Ò... where a, b, c, n are
(finite) integersÓ (with the finite added for emphasis). If you remove
this last phrase, then the FLT that most mathematicians think of would
then have to be called ÒFLT for integersÓ. It is true that FLT is false
for p-adics, matrices, quaternions, and a lot of other number systems.
In this sense, there are counter examples to the general FLT. But there
is no counter example to FLT (integers): this was proved by Wiles.
> The whole world will laugh hysterically if Wiles gets approval
>and Ludwig Plutonium comes up with the counterexample. Which
>choice would you pick--- a 1000 page math community accepted
>(fake) proof, or a counterexample? So far my confidence in the math
>community is that they would prefer the 1000 page ordeal.
There seems to be a point you keep missing. If you change the
definitions of terms (like integer, real, etc), then theorems change as
well. Thus,
ÒFLT for normal integersÓ (Wiles)
is a different theorem than
ÒFLT is not true for 10-adic integersÓ (proved by many people)
and both results (admittedly one is very long, the other very short),
are good mathematics and knowing one does not automatically get you the
other result. So there is no real irony, except that theorems that hold
for one number system need not hold for all number systems.
Of course, you may dispute that the commonly accepted definition of
ÒintegerÓ SHOULD be the commonly accepted definition. But even if you
replace the concept of integer, the ÒoldÓ concept of integer is still a
valid one, so you canÕt just blithely say (for example) Òwell, if I
redefine integers to be 10-adic, so the reals are now equal cardinality
to the integers, then there is no infinite set with smaller cardinality
than the reals anymoreÓ, because the ÒoldÓ notion of integer still
exists.
Terry
-------------------------------------------------------------
Newsgroups: sci.math
From: Ludwig.Plutonium@dartmouth.edu (Ludwig Plutonium)
Subject: Re: Fermat's Last Theorem
Message-ID:
Organization: Dartmouth College, Hanover, NH
References:
<278vgj$pi2@paperboy.osf.org>
<27glo6$elj@paperboy.osf.org>
Date: Mon, 20 Sep 1993 15:39:46 GMT
Lines: 15
In article <27glo6$elj@paperboy.osf.org> karl@dme3.osf.org (Karl Heuer)
writes:
>In article >Ludwig.Plutonium@dartmouth.edu (Ludwig Plutonium) writes:
>>does this above monster 4N=N^4 repeat in a block like Rational >>numbers repeat
>
>No, it doesn't.
Karl is this new number which you discovered (if you do not have a
name for it as yet, I suggest HeuerPu Numbers, but that is up to you)
analytic irrational or transcendental? Given that concepts of
transcendental can be translated to P-adic.
Also, please tell me if there is a mirror reflection in the Reals of
HeuerPu Numbers. Is there a Real number between 0 and 1 which has
HeuerPu properties?
-------------------------------------------------------------
EMAIL
Date: Tue, 21 Sep 93 00:01:54 EDT
From: ÒKin ChungÓ
To: Ludwig.Plutonium@Dartmouth.EDU
Subject: INFINITE INTEGERS
In-Reply-To:
Organization: Princeton University
Cc:
Before you embrace the so-called Òinfinite integersÓ too closely,
consider this straightforward sum:
....9999999999999999999999999999999999999999999999999
+....0000000000000000000000000000000000000000000000001
___________________________________________
....000000000000000000000000000000000000000000000000
Using your identification of the (finite) integers with a subset of the
infinite integers, this shows that (-1) = ...9999. Do you see what IÕm
trying to get at?
-------------------------------------------------------------
From: karl@dme3.osf.org (Karl Heuer)
Newsgroups: sci.math
Subject: Re: Fermat's Last Theorem
Date: 21 Sep 1993 20:59:42 GMT
Organization: Open Software Foundation
Lines: 25
Message-ID: <27npvu$blc@paperboy.osf.org>
References:
<27glo6$elj@paperboy.osf.org>
In article
Ludwig.Plutonium@dartmouth.edu (Ludwig Plutonium) writes:
>(if you do not have a name for it as yet, I suggest HeuerPu Numbers,
>but that is up to you)
I've been calling N^k=k*N the "LP equation". I don't think its
solutions need names of their own, but "LP numbers" will do for now.
> Karl is this new number which you discovered analytic irrational or transcendental? Given that concepts of transcendental can be translated to P-adic.
It's easy to prove that it's irrational, because the rationals have the
same properties in the 10-adic numbers that they do in the reals. Since
it's a zero of the polynomial x^k-k*x, it's a (non-Real) irrational
algebraic number.
>Also, please tell me if there is a mirror reflection in the Reals
The LP equation has real solutions for all k; e.g. sqrt(3) for k=3.
(As someone else already noted, these solutions will have magnitude
>1.)
There are similarities to the Reals, but it's not just a renaming. 1/3
exists as a (repeating) 10-adic integer, but it's not . . .3333; it's .
. .66667 instead. (Multiply it out: . . .66667 * 3 = . . .00001 no
matter how many places you carry it to.) Also, x^2 = 3 has a solution
in the Reals but not in the 10-adics; while x^2 = -31 has a solution in
the 10-adics but not in the Reals.
-------------------------------------------------------------
From: karl@dme3.osf.org (Karl Heuer)
Newsgroups: sci.math
Subject: Re: P-ADIC NUMBERS: RENAMED AS INFINITE INTEGERS
Date: 21 Sep 1993 21:14:12 GMT
Organization: Open Software Foundation
Lines: 12
Message-ID: <27nqr4$bpe@paperboy.osf.org>
References:
In article
Ludwig.Plutonium@dartmouth.edu (Ludwig Plutonium) writes:
> Let us rename the math subject "P-adic Numbers" to that of
>"Infinite Integers."
I'd rather keep the existing terminology. There are several consistent
models of arithmetic that include objects that look "infinite" in some
sense: the Hyperintegers/Hyperreals, the Surintegers/Surreals, the
compact number line, the Riemann sphere, the transfinite ordinals, the
transfinite cardinals, etc.
The only thing that's "infinite" about the p-adic numbers is their
representation as a digit string, and that's analogous to the infinite
number of digits in a non-terminating Real.
-------------------------------------------------------------
Newsgroups: sci.math
From: Ludwig.Plutonium@dartmouth.edu (Ludwig Plutonium)
Subject: Re: P-ADIC NUMBERS: RENAMED AS INFINITE INTEGERS
Message-ID:
Organization: Dartmouth College, Hanover, NH
References:
<27nqr4$bpe@paperboy.osf.org>
Date: Thu, 23 Sep 1993 16:34:43 GMT
Lines: 17
In article <27nqr4$bpe@paperboy.osf.org>
karl@dme3.osf.org (Karl Heuer)
>I'd rather keep the existing terminology. There are several >consistent models of arithmetic that include objects that look >"infinite" in some sense: the Hyperintegers/Hyperreals, the >Surintegers/Surreals, the compact number line, the Riemann >sphe,
the transfinite ordinals, the transfinite cardinals, etc.
>
>The only thing that's "infinite" about the p-adic numbers is their
>representation as a digit string, and that's analogous to the infinite
>number of digits in a non-terminating Real.
How about TRANSFINITE INTEGERS? Any objections?
I am trying to give a good name to these infinite strings for
another assault on CantorÕs claim that there are more than one type of
infinity.
-------------------------------------------------------------
From: "Terry Tao"
Subject: Re: Wiles proof of FLT
To: Ludwig.Plutonium@Dartmouth.EDU (Ludwig Plutonium)
Date: Sun, 26 Sep 93 17:10:49 EDT
In-Reply-To: <5509284@blitzen.Dartmouth.EDU>; from "Ludwig Plutonium"
at Sep 26, 93 5:07 pm
>
> Terry tell me if all P-adic numbers have inverses. Can you prove it
>
If P is prime, then all numbers which are not multiples of P have
inverses. (in other words, all numbers whose last digit is not 0.)
If P is not prime, then all numbers which are coprime to P have
inverses, i.e. the last digit of that number is coprime to P.
To prove it, it is sufficient to show that you can invert the last N
digits, for each N. This is a standard exercise in modular arithmetic.
Terry
p.s. I would still like to hear your comment on my proof that there
must be a counter-example to FLT. Do you think my proof is flawed?
-------------------------------------------------------------
EMAIL
From: ÒTerry TaoÓ
Date: Tue, 28 Sep 93 20:34:10 EDT
To: Ludwig.Plutonium@Dartmouth.EDU
Subject: Re: FermatÕs Last Theorem
Newsgroups: sci.math
In-Reply-To:
References: <2728f8$51j@news.u.washington.edu>
<278vgj$pi2@paperboy.osf.org>
Organization: Princeton University
Several observations.
(1). In my mind, the reason why 2 is exceptional in FLT is not because
2x2 = 2+2, but rather because 2 is even. If n is odd, then FLT can be
rewritten in the much more beautiful
u^n + v^n + w^n is never 0 unless uvw is 0 (where u,v,w are integers).
(2). P-adic counter-examples to FLT have been known for some time -
almost at the same time that they were discovered. P-adics are like
real numbers, in a sense: who's interested in a real number
counter-example to FLT?
(3). Wiles uses special properties of the finite integers that the
infinte integers do not have, one of which is that there are infinitely
many primes in the finite integers.
(4) Your statement "Wiles's proof contradicts the Fourier theorem" is
indirect non-existence - after all, that's what you said when I used
the same principle to show that FLT must be false for finite integers.
(5) FLT is true for finite integers, false for p-adic integers. Each
finite integer is a p-adic integer, but the set of finite integers is
only a SUBSET of the set of p-adic integers. They are different things,
and you have two different FLTs for two different number systems. FLT
is assumed to be over the finite integers unless otherwise specified,
so your statement that ÒAll proofs of FLT are fakeÓ is wrongly deduced.
However, you have made a true deduction in saying that no proof of FLT
can rely purely on algebraic manipulation, because of the p-adic
counter example. It must use a property that the finite integers have
but the infinite integers do not, for example
(a) induction;
(b) infinitude of primes;
(c) no zero divisors (WillÕs two numbers, a and b, multiply to 0)
etc.
Terry
-------------------------------------------------------------
EMAIL
From: ÒTerry TaoÓ
Subject: Re: Fermat's Last Theorem
To: Ludwig.Plutonium@Dartmouth.EDU (Ludwig Plutonium)
Date: Tue, 28 Sep 93 22:22:46 EDT
In-Reply-To: <5569918@blitzen.Dartmouth.EDU>; from "Ludwig Plutonium"
at Sep 28, 93 10:18 pm
>
>--- You wrote:
>However, you have made a true deduction in saying that no proof of >FLT can rely purely on algebraic manipulation, because of the p-adic >counter example. It must use a property that the finite integers >have but the infinite integers do not, for
example
>--- end of quoted material ---
>Thanks that is important I needed that.
>
>Terry tell me if there is a Real analog of that number Karl produced. >Karl says it is greater than 1. Can you pinpoint it better.
>
the cube root of 4.
Terry
-------------------------------------------------------------
EMAIL
From: ÒWilliam SchneebergerÓ
Subject: Re: your counterexample posting
To: Ludwig.Plutonium@Dartmouth.EDU (Ludwig Plutonium)
Date: Wed, 29 Sep 93 12:10:41 EDT
In-Reply-To: <5581074@blitzen.Dartmouth.EDU>; from ÒLudwig PlutoniumÓ
at Sep 29, 93 11:39 am
Sorry, I don't have a copy. But here's the deal:
We solve a == 0 (mod 5)
a == 0 (mod 25)
a == 0 (mod 125)
.
.
.
and
a == 1 (mod 2)
a == 1 (mod 4)
a == 1 (mod 8)
by the Chinese Remainder Theorem. Similarly we solve
b == 0 (mod 5)
b == 0 (mod 25)
b == 0 (mod 125)
b == 0 (mod 625)
.
.
.
and
b == 1 (mod 2)
b == 1 (mod 4)
b == 1 (mod 8)
.
.
.
Now one can prove that a*a=a, b*b=b, a*b=0, a+b=1. This leads
immediately to the fact that, for all (finite natural numbers) n,
a^n + b^n = c^n where c == 1.
There are, however, much more interesting solutions to FLT in these
numbers. The above solution may well be considered trivial as abc == 0.
For the p-adic numbers (infinite integers in a prime base p) the above
solution does not exist. But I know that there do exist solutions for n
relatively prime to p(p-1).
Will
-------------------------------------------------------------
EMAIL
From: ÒTerry TaoÓ
Subject: Re: Schneebergers post
To: Ludwig.Plutonium@Dartmouth.EDU (Ludwig Plutonium)
Date: Wed, 29 Sep 93 14:45:31 EDT
In-Reply-To: <5581425@blitzen.Dartmouth.EDU>; from "Ludwig Plutonium"
at Sep 29, 93 11:55 am
>
>Hi Terry. I lost Schneebergers post of counterexamples. Would you >have a copy? Please relay
>
I haven't got that post either, but here's how you can compute them:
The idempotents of the 10-adics are the solutions of a^2 = a. Thus
their first digit must be 6 or 5 (by considering the problem modulo 10)
- the idempotents 0 and 1 being discounted. Let us, say, consider the
one with last digit 5: they sum up to 1 anyway.
You can compute successive digits iteratively. If the next digit is a,
i.e. the last two digits are 10a+5, then the last two digits of the
square is 25, so a must be 2.
Similarly, if we let the next digit be b, so the last three digits are
100b + 25, then the last three digits of the square is 625, hence b =
6. And so on.
Terry
-------------------------------------------------------------
EMAIL
From: ÒTerry TaoÓ
Subject: Re: Schneebergers post
To: Ludwig.Plutonium@Dartmouth.EDU (Ludwig Plutonium)
Date: Wed, 29 Sep 93 15:02:53 EDT
In-Reply-To: <5581425@blitzen.Dartmouth.EDU>; from "Ludwig Plutonium"
at Sep 29, 93 11:55 am
Actually, all you need to do is take 5 and keep squaring it. The powers
of 5 will converge in the 10-adic topology to one of Will's numbers.
(recall: whereas the metric in say the reals, is |x-y| for the distance
between x and y, the metric between two p-adics x and y is 1/p^n, where
n is the highest number of times that p divides x-y.)
Terry
-------------------------------------------------------------
EMAIL
From: ÒWilliam SchneebergerÓ
Subject: Re: your counterexample posting
To: Ludwig.Plutonium@Dartmouth.EDU (Ludwig Plutonium)
Date: Wed, 29 Sep 93 15:21:43 EDT
In-Reply-To: <5581838@blitzen.Dartmouth.EDU>; from ÒLudwig PlutoniumÓ
at Sep 29, 93 12:15 pm
So, I guess, some solutions for exponent 3 are
a == 1
b == 10
c == . . .52979382777667001
a == 1
b == 20
c == . . .4437336001
a == 1
b == 30
c == . . .4919009001
In fact for any finite n, a == 1, b a multiple of 10, we can solve the
equation of FLT.
But, look, all IÕve shown here is that in the 10-adic numbers there is
a solution to the equation. I have _not_ contradicted the statement of
FLT which says that there is no solution among the usual finite
integers. This is more of a problem.
Later.
-------------------------------------------------------------
Newsgroups: sci.math
From: Ludwig.Plutonium@dartmouth.edu (Ludwig Plutonium)
Subject: Re: Wiles's proof of FLT
Message-ID:
Organization: Dartmouth College, Hanover, NH
References: <27st80$asv@clipper.clipper.ingr.com>
Date: Wed, 29 Sep 1993 16:24:55 GMT
Lines: 15
In article
Ludwig.Plutonium@dartmouth.edu (Ludwig Plutonium) writes:
>FLT was outstanding because there is no proof of FLT in the general >case. The general theorem of FLT has no proof because transfinite >integers are just as real as finite integers. All attempts at a proof >of the general equation of FLT are doomed to
failure.
PROOF OF FLT. The general form of FLT where a^n+b^n=c^n are such
that the four numbers a,b,c,n could be transfinite integers as well as
finite integers. Hence a proof in the general case is impossible. The
counterexamples in the P-adics is the proof. Anything else would have
to restrict the four numbers a,b,c,n to finite number cases and show
that in those restrictions there are no P-triples. QED
Subject: Re: looking for any position
From: raven@david.silesia.pik-net.pl (Grzegorz Kruk Ph.D.)
Date: 14 Nov 1996 02:40:56 GMT
Grzegorz Kruk Ph.D. (raven@david.silesia.pik-net.pl) wrote:
ADDRESS:
Grzegorz Kruk, Ph.D.
Wysoka 12A/146
41-200 Sosnowiec
Poland (please register mail)
^^^^^^^^^^^^^^^^^^^^
or ph./fax/modem (2400-8-N-1) +48 32 1995546
EDUCATION:
Ph.D.
13th of December 1993, graduated from Trinity
College, University of Dublin, Ireland.
Thesis: FT Infrared Spectroscopy of Liquid Crystals.
Papers:
A. Kocot, R. Wrzalik, G. Kruk, J.K. Vij, Molecular Materials, v.1,
p.273-279, (1992).
A. Kocot, G. Kruk, R. Wrzalik, J.K. Vij, Liquid Crystals, v.12, n.6,
p.1005-1012, (1992).
J.K. Vij, A. Kocot, G.Kruk, R. Wrzalik, R. Zental, Mol. Cryst. Liq. Cryst.,
v. 14, p. 337-350, (1993).
G. Kruk, A. Kocot, R. Wrzalik, J.K. Vij, O. Karthaus, H. Ringsdorf, Liquid
Crystals, v.14, n.3, p.807-820, (1993).
G. Kruk, J.K. Vij, O. Karthaus, H. Ringsdorf, Supramolecular Science, v.2,
p.51-58, (1995).
6th of July 1989, graduated from Silesian University, Katowice, Poland,
(specialization: experimental and applications of physics).
Degree of Magistri (Master) in Physics.
M.Sc. Graduation Exam: "A"
Total Grade Point Average "B" (4.0)
Thesis: Strong Thermal Lens Induced by Laser Light in Mixtures of
Organic Liquids with Ferrocene.
Published in Berichte der Bunsenges. Phys. Chem., v.94, p.417-420, (1990)
by G. Kruk and Z. Gburski.
INTERNATIONAL MEETINGS:
Internal EC SCI*0291 project meeting, 1990, University of Dublin, Ireland.
14th International Liquid Crystal Conference, 1991, Pisa, Italy,
(Presented 2 posters).
Internal EC SCI*0291 project meeting, 1992, University of Manchester,
U.K., (Seminar).
WORK EXPERIENCE
1988-1994 physicist, Silesian University, Katowice, Poland.
Duties:
1) preparing and explaining basic experiments on physics for
undergraduate students.
2) writing computer programmes for experiments
3) designing and performance supervising of new experimental
setups for experiments within undergraduate course
4) supervising students performing their own experiments
5) supervising maintenance jobs on experimental hardware
6) assembling electronic hardware for experiments like e.g.
interfaces for meters and also writing software in ASSEMBLER
1989-1990 part time teacher of programming in PASCAL and BASIC, III Liceum
Ogolnoksztalcace im. A. Mickiewicza, Katowice, Poland.
Duties:
1) Installing software
2) Teaching programming in Pascal and Basic and also how to
run and operate other applications
1991-1993 research student, EEE Department, Trinity College, University of
Dublin, Dublin, Ireland. (working for EC research project SCI*0291
in cooperation with groups of University of Mainz and University of
Manchester).
Duties:
1) Laboratory research on liquid crystals and discotic liquid
crystals using FTIR spectroscopy equipment and polarizing
microscopy including:
a) FTIR Spectrometer BIO-RAD FTS60A a Motorola 68000 based
system with IDRIS operating system
b) Programmable Intelligent Temperature Controller
Oxford ITC4
2) Writing software applications for data handling in FORTRAN
3) Data handling and plotting on VAX/VMS (MATLAB), UNIX, DOS
(EASYPLOT, WORD, LOTUS MANUSCRIPT)
4) Preparing seminars for internal project meetings and conferences
5) Correcting tutorials
6) Supervising students working with MATLAB during first course of
Digital Signal Processing
03.1994 - Owner of "RAVEN" -Translation & Interpreting Services Bureau.
Cooperating with:
East Europen Business Centre, Welling, London, Kent
International Language Engineering, Boulder, CO, USA (signed
contract)
Duties:
1) Manager
2) Accountant
3) Translator
4) Writing and modifying own software for accountancy
PROGRAMMING: PASCAL, FORTRAN, C
EXPERIENCE WITH OPERATING SYSTEMS: VMS, UNIX, DOS, RSX-11, CP/M, TOS,
LANGUAGES: English-fluent, Polish-native.
OTHER SKILLS: driving licence, yacht steersman licence
INTERESTED IN: programming, robotics, computer simulations, AI,
optical computing, OB, optical transistor, space research.
OTHER FIELDS OF INTEREST: sailing, skiing, sport driving, basketball, swimming,
movies, chess.
already 33 y.o. (born on July 27th, 1963) , married, 2 children.
REFERENCES:
Prof. H. Robinson-Hammerstein, Trinity College, Dublin 2, Ireland
ph. +353-1-7021045
Prof. J.K. Vij, EEE Department, Trinity College, Dublin 2, Ireland.
ph. +353-1-7021431