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Jun 30, 2009, 11:23:22 AM6/30/09

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Please notice that my book "Associative Digital Network Theory"

was just released by Springer Verlag, see :

http://www.springer.com/computer/communications/book/978-1-4020-9828-4

was just released by Springer Verlag, see :

http://www.springer.com/computer/communications/book/978-1-4020-9828-4

It is about the use of function composition (semigroup theory) as

binding principle for the three main levels of functions applied in

computer engineering : State-machines, Arithmetic and (Boolean)

logic, corresponding to a hi�rarchy of associative algebra's :

non-commutative, commutative, and idempotent,

respectively : a(bc)=(ab)c=abc , ab=ba , aa=a.

In Chapter 2 the five basic state machines are derived, and

the decomposition of permutation machines with a non-trivial

simple group as closure is in Ch.3 (e.g. group A5 of order 60

as coupled network of cyclic groups of order 2 [twice] , 3, 5).

Ch.4 discusses the general decompositon of finite semigroups /

statemachines, as (possibly coupled) network of the five basic

statemachine types, including the two non-commutative

memory types: branch- and set/reset machines.

'Planar Boolean Logic' (Ch.5) is defined as practically related

to symmetric Boolean functions, with a proof that all BF_n of

n<5 inputs are planar. Also various forms of fault tolerant logic

designs are treated and compared.

Moreover, proofs of FLT and Goldbach's Conjecture (Ch.8, 9)

are given, both using a 'residue-and-carry' method (with proper

choice of modulus), as well as a result of "Waring for residues"

(Ch.10) for prime power moduli: each residue mod p^k [k>0] is

the sum of at most 4 p-th power residues.

Log-arithmetic (Ch.11) over double base 2 and 3 is discussed ,

using : each odd residue mod 2^k is a unique signed power of 3,

as well as over single base 2 (a 32-bit VLSI implementation as

an Euro 'Esprit' project).

-----

dr. Nico F. Benschop, Geldrop (NL) -- Amspade Research ----

nfben...@onsbrabantnet.nl

[mod note. Springer have clearly published this book by Benschop.

Furthermore, this book claims to give elementary proofs of FLT

and of Goldbach's conjecture. Benschop has posted proofs of

such things in the past---for example chapter 8 of this book

appears to the moderator to be largely the same as the proof

of Goldbach's conjecture announced at

http://arxiv.org/abs/math/0103091

in 2001. As far as the moderator knows, the mathematical community

has not yet accepted the proof described in this paper. Furthermore, viewers

with access to math. reviews might want to see review number MR1831809, which

appears to the moderator to pertain to another chapter of this

book. The moderator wants to make it clear that acceptance of

this sci.math.research post is nothing more than *acknowledgement of the

statement that Springer has published the book*, which the moderator

believes to be of independent interest, and does not imply that

the moderator has read, or believes, any of the stronger claims

made in the book.]

Jul 1, 2009, 6:30:02 AM7/1/09

to

On 30 June, 16:23, Nico Benschop <nfbensc...@onsbrabantnet.nl> wrote:

> Please notice that my book "Associative Digital Network Theory"

> was just released by Springer Verlag, see :http://www.springer.com/computer/communications/book/978-1-4020-9828-4

> Please notice that my book "Associative Digital Network Theory"

> was just released by Springer Verlag, see :http://www.springer.com/computer/communications/book/978-1-4020-9828-4

At �81.50 for 180 pages I cannot see this being a bestseller.

I see that this is published by the computer science division

rather than the mathematics division of Springer. I wonder

if the manuscript was reviewed by any competent mathematicians.

> Moreover, proofs of FLT and Goldbach's Conjecture (Ch.8, 9)

> are given, both using a 'residue-and-carry' method (with proper

> choice of modulus), as well as a result of "Waring for residues"

> (Ch.10) for prime power moduli: each residue mod p^k [k>0] is

> the sum of at most 4 p-th power residues.

There we are. A decade or so ago when both Mr Benschop

and I were active in sci.math, Mr Benschop had a reputation

as one of the group's leading "cranks", promulgating his bogus

"proofs" of Fermat's last theorem and Goldbach's conjecture.

I, and others, kept refuting these arguments, at least those

which were clear enough to be refuted. I would be sceptical

whether there is any value in this new book, but I'm not paying

to find out.

A copy of the bibliography and index of the book can be

downloaded from the web link above. I note that one of the papers

cited was Benschop's 2000 paper in the journal "Computers and

Mathematics with Applications". In this paper Mr Benschop

claimed to prove that there was no prime p with 2^p = 2 (mod p^3).

However the alleged proof was bogus and was refuted to me in

a letter to the editor of the journal. Those with access to

MathSciNet can consult

http://www.ams.org/mathscinet/search/publdoc.html?pg1=IID&s1=316210&vfpref=html&r=22&mx-pid=1831808

to see the saga.

But while the book cites Benschop's paper it does not cite my

refutation. I consider this to be both dishonest and cowardly

of Mr Benschop.

Robin Chapman

[mod note: I think Benschop and Chapman have had previous disagreements

about Benschop's claimed results before. I don't want this thread to

turn into a s.m.r. flame war so, now I've let both sides have "one turn"

I've set followups to sci.math; s.m.r. is definitely no place for a debate about

whether Benschop has proved Goldbach or not. ]

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