Musatov checks in with Cern: trying not to blow up the net privatizing it with his mmm.[domain].web™
gratis-_+_8_Sum_
[domain].web=99 =3D (TM) network based mmm.[domain].web™
> [and here is what I sent to Cern]
Hello,
I'm sorry for jumping right into it -- but for me it would be less!
I am building a mmm.[domain].web™ = (TM) network based on
== The Effect of Math Loops on Polynomial-Time Reductions ==
[http://groups.google.com/group/sci.math/browse_thread/thread/
29b0aa06aff2fa68#
USENET]:
On Sep 15, 12:05 pm, ©2009 Martin Musatov. <marty.musa...@gmail.com>
wrote:
1+0=1+1==2+0=2+1==3+0=3+1==4+0=4+1==5+0=5+1==6+0=6+1==7+0=7+1==8+0=8+1==9+0=9+1==10=1+0+9=10+1==11=2+0+9=11+1==12=3+0+9=12+1==13=4+0+9=13+1==14=5+0+9=14+1==15=6+0+9=15+1==16=7+0+9=16+1==17=8+0+9=17+1==18=9+0+9=18+1==19=9+0+9+0+1=19+1==20=9+0+9+0+2=20+1==21=9+0+9+0+3=21+1==22=9+0+9+0+4=22+1==23=9+0+9+0+5=23+1==24=9+0+9+0+6=24+1==25=9+0+9+0+7=25+1==26=9+0+9+0+8=26+1==
0 1a 2b 3c 4d 5e f6 g7 h8 i9
j10 k11 l12
m13 n14 o15
p16 q17 r18
s19 t20
u21 v22
w23 x24
y25 z26
0
1a 2b 3c 4d 5e f6 g7 h8
i9 j10 k11
l12
m13 n14 o15
p16 q17
r18
s19 t20
u21 v22
w23 x24
y25 z26
mmm.[domain].web™ c o m i n g s o o n f r o m M e A m I (TM)
http://MeAmI.org
'Search for the People'
I would like some help and knowledge base on execution of this process
to minimize any [not] intrusions on the www.[domain]s
I am writing as a courtesy mid-build and understand the basic
processes quite well but the implications systems wide seem
complicated.
I would appreciate any advice and guidance from the community at
large.
Thank you for your time.
Martin Musatov
http://MeAmI.org
tel: 818.430.4586
Post Scriptum="after written": I am also implementing e+mail™^(TM)
PPS. = post post scriptum: But the primary issue is the net.
[LINK] == http://www.meami.org
building. Though you may not be able to in all fairness just judge
haphazardly a book by the cover it has you may often times understand
a great deal about what might be in a building by what is outside of
the building. Computations are no exception. Sunlight travels 93
billion miles to riped fruit.
--M. Michael Musatov
Step Forward Backward
Backward Step Forward
7+17+10=34
1234567891011121314151617
17*2=34
17+17=34
-17
+17
/34 + 17 _
In:atmiacnisimollisposu:out
In: Translations
abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ
i n
a t
m:
i
a
c
n
i s
i n
a t
m:o
l
l
i s
p
o s u
e r
e vwxyzABCDEFGHIJKLMNOP
r
a e s
e n t v
e n
e n
a n
n t
i s
e r
a t
n
e
c v
u
l p u
t
a t
e m o
l
e st
i
e
e
l
i t
f
e l
i s
d i
c tu
m
l
e o
no
n
f
a u
c i
b u
s
r
i s u
s
e r
a t
in: of r :: out of
P: ra :: out of
s: :: out of
n: tv :: out of
n: :: out of
n: atis :: out of
r: at
n: :: out of
c: vulputate :: out of
m: ol :: out of
s: ti :: out of
h: :: out of
l:itf :: out of
l:isdictuml :: out of
o:nonfaucibusrisus:: out of
r:at
Powered by MeAmI.org (C) = Copyright == Copywrite(C) 2009. MeAmI.org
M.Michael Musatov
@ECHO ECHO
ECHO Hello World! @ECHO
ECHO Hello Universe! @EcHO
ECHO P = NP Quod Erat Demonstrandum! (C) 2009. http://meami.org
@\windows\ie7\iexplore.exe meami.org
@"c:\program files\internet exploder\
iexplore.exe 'http:// www.meami.org'"
@open http:\\www.meami.org"
#include
void main (void)
{
ShellExecute (NULL, "open", "http://www.meami.org", NULL, NULL,
SW_SHOWNORMAL);
}
@ECHO http://MeAmI.org
ECHO http://MeAmI.orgarguments in the open class \/*****************
code: copywrite=(c_) 2009@ECHO HELLO WORLD
write in quit: sp{or}mi .org{an}do{no}restlesstestsrealcan#
[LINK] == http://www.meami.org
building. Though you may not be able to in all fairness just judge
haphazardly a book by the cover it has you may often times understand
a great deal about what might be in a building by what is outside of
the building. Computations are no exception. Sunlight travels 93
billion miles to riped fruit.
--M. Michael Musatov
Step Forward Backward
Backward Step Forward
7+17+10=34
1234567891011121314151617
17*2=34
17+17=34
@ECHO ECHO
ECHO Hello World! @ECHO
ECHO Hello Universe! @EcHO
ECHO P = NP Quod Erat Demonstrandum! (C) 2009. http://meami.org
@\windows\ie7\iexplore.exe meami.org
@"c:\program files\internet exploder\
iexplore.exe 'http:// www.meami.org'"
@open http:\\www.meami.org"
}
@ECHO http://MeAmI.org
ECHO http://MeAmI.orgarguments in the open class \/*****************
code: copywrite=(c_) 2009@ECHO HELLO WORLD
ECHO HELLO WORLD
FILE ROOT: P==NP Quod Erat Demonstandum.txt - Notepad
conta:in language l {m}
/tardir/tiffs/A354475.tiff This is the html version of the
file
http://handle.dtic.mil/100.2/ADA354475.
Invoke :
http://MeAmI.org
web.{
Page 1
{ri RECORD COPY>TS: 60-11,353 MAIM. FILE JPRS: 23269 March 1?60fX}
REALIZATION OF
FUNCTIONS OF SUPERPOSITIONS- USSR -by R. Ye. Krichevskiy {pi}
{PBTWBDTION ¿TATOMECf
XApproved for pahlie r«i*ca»j Dirtribattoa Unlimited Distributed by:
OFFICE OF
TECHNICAL SERVICES U. S, DEPARTMENT OF COMMERCE WASHINGTON 25, D. C.
{OTIC} QUALITY
{Ora} PB {C} I {l} D 4U. S, JOINT PUBLICATIONS {{{R
{E}{{
SEARCH}
}
}
}
}
SERVICE 205 EAST
{U} 2nd STREET, SUITE
300 NEW YORK 17, N. Y.
Reproduced From Best Available Copy
Page 2
!@v
@backward:write{Proof (P = NP)
}
{JPRSî 2326OSO: 3292~ff;ÏZATïON Of FUNCTIONS OP SïIFBRPOSÏÏIOF/""ï}
This is a translation of an article written
{"}
by
B.Ye,
Krichevskiy in Problem
{y libar netiki
(E)
P
{Problems of Cyber-netics}
,
Ho 2, Moscow, 19591
{P&S©® 123-138^/ |_Jn}
the
-the or{y}
of controlling systems and in math
{e-»iirfciftfl.1 Icwric}
we frequently encounter the problem of the
{¿¿¡ api}
best expression or realization of the given function by
{¿eane}
of
{'}
con
{e}
tract
{ions}
of one or another type
{*}
for ex
{-}
ample, "by means of
itérât
{ions}
(superpositions) of some,
{,}.
basic functions or "by means of Controlling systems. The construction
is usually ascribed
{¿n}
index of simplicity which
{ssxidly}
expresses its complexity, for example, the number contacts in the
{oontaet}
circuit or the number of letters in the formula
{?}
the simplest of the constructions which expresses the function is th
{@}
has a minimum index of
{"simplicity«}
{
}
A substantial characteristic of the mass of the functions
{öf} {Du}
is the number
{L(Ik)—the .}
upper edge of the indexes of the simplest constructions express the
functions of
{%?}
this number was, for the first time.
{_ ^}
brought up by Hiordan and Schannon
{f±Ji »chanaon ¿ '¿J.}
Many works deal with the evaluation of
{l(ï>h) iß}
the con
{-}
crete selection of the mass
{Du}
,
the mass of realizing con
{-}
structions and the
{.}
Index of simplicity
{? m}
wish to mention the papers by Schannon
{/""2 7,}
Riordan and Schannon
{¿ l_/sLupanov f'l 7,}
TablonskTy
{¿4 J7,}
Povarov
{¿5, 6J.}
In the work
{/TT»}
the constructions
{'}
of a very general type are examined as the constructions express the
given function
{* ^}
{„}
We shall examine the
{»}
superpositions of elementary objects
{"}
as the constructions
{,}
.
The concept of the super-position of elementary objects is introduced
{•}
as a genera
{-}
lization of the concept of the superposition of basic functions and
makes it possible to obtain uniformly re
{-}
su i
{[l]}
ts pertain
to the theory of circuits and to the algebra of logic. It ör the index
of
simplicity we require the fulfillment of natural limitations (see p.
1. 3
(The first figure indicates the number of the paragraph; the second,
the number of
the point.}. Under these conditions, the lower evaluation for
[!{%)]
is obtained:
We wish to note that the Lupanov method would give here a much coarser
evaluation
because Lupanov examined constructions of a more general type than, in
our ease.
P==BoiEEEPwc^3&
Page 3
{' JPRS: 2326OSO: 3292-ÎTT^AIilZATlÒN O? MFKCTIONS Oï
SUPERPOSITIONS/"ÌChist} is a
translation of an article written by E.Ye. Erichevskiy in Problem{y
Kibernetiki}
(Problems of Cyber-netics), lío 2, Moscow, 1959» pages 123-138*7 ---In
the
theory of controlling systems and in mathe{-}matics{!} logic we
frequently encounter
the problem of the {„} amplest expression or realization of the gíve
{®n} function by
means of constructions of one or another type, for ex{-}ample, by
means of
iterations (superpositions) of some, basic functions or by means of
controlling
systems. The construction, is usually ascribed {¿n} index of
simplicity rapidly
expresses its complexity, for example, the number contacts in the {o}
on tractable
circuit{s} or the number of letters in the formula {?} the simplest of
the
constructions expresses the function has a minimum index of
simplicity. A substantial
characteristic of the mass of the functions of {%} is the number {!(%)
—} the upper
edge of the indexes of the simplest constructions which express the
functions of {%» ^}
is number was, for the first time, brought up by Hiordan and Schannon
{£^lj$} Schannon
{¿~2j}. Many works deal with the evaluation of {LfDu)} in the con{-}
crete selection of
the mass {Dv,} the mass of realizing con{-}structions and the index of
simplicity; we
wish to "mention" the papers by Schannon {/"2 7»} Riordan and Schannon
{¿\y,Lupanov ¿jlj/},
Yablonskiy {¿4~7*} Bivarov {/5f 6J}, {I} in the work {P¿fXT» ^e}
constructions of a very
general type are examined as the constructions express the given
function. We shall
examine the "superpositions of elementary objects" as the
constructions. The concept
of the super-position of elementary objects is introduced as a
generalization of the
concept of the superposition of basic functions and makes it possible
to obtain
uniformly results {s} [re: {-suits{l}\] pertain to the theory of
circuits and to the
algebra of logic. From the index of simplicity we require the
fulfillment of natural
limitations (see p. 1. 3 (The first figure indicates the number of the
paragraph}
the second, the number of {thß{} point.{).} Under these conditions,the
lower
evaluation for L(%) is obtained! we wish to note that the Lupanov
method would
give here a much coarser evaluation because Lupanov examined
constructions of a
more,general type than in our case,
Page 4
Determination 1 (inductive). Any symbol from ,.as is Icalled
superposition of
class 0.2, Let 4«cCA> *■••*"Al be called the superposition ofclass «■-
If »^%
and all 4«~ —superpositions of a classless than ■■», moreover, the
maximum of
the classes of thesuperpositions A,,J»»*,..... ....... ..$, is equal
to
n—I-Superposition the class of which is not less than 1is called
superposition
of elementary, objects of *S . The.mass of superpositions of the
objects is
designated by"*:'; Examples of the superposition of class 1 are, for
the pro-
■"'per slection of the masses ,;*«ìkì4#£«{£*>:An example of
superposition of
class 2 is ; £*(£»(*»• *** *v *A *t* *»>*1,2. Geometric
illustration.'
Henceforth, it'""will be convenient to utilise the geometric
interpretation
ofsuperposition. We shall determine inductively the image of
superposition, its
root, and its end segments. We shallconsider an «¿—place star as the
àmage of an
.%-place superposition of class I /.*(*,,...,'x#) ; i. e., the combina-
tion of
the %-M segments which emanate from one point,one of which, called the
root, is
separated, while the re-maining, called ends, are numbered in a
definite
order.We shall compare the root with the symbol £<■ and the i-thsegment
—with the
symbol *i (Pig 1).Let there now be the superposition of elementary
objects of
n-th class '£*£*$. • •..■<%,), where ^ are the super-positions of the
classes
not higher thanl*--? r; /«I,..., $K. Let us assume that for the
superposition Ait
"a geometric image has already oeen constructed and thatthe symbol
i^,
corresponds to the root of it and the sym-bols av, encountered in the
superposition of a(. corres-pond to the end segments.In order to
construct the
giometric image .¿»(-a»...".",. A s^)we shall identify the i-th end
segment of
the star, corres-ponding to M*x » **:«■»■a»¿ with the root of the
image of 4.and
for the resulting segment we shall accordingly place the symbol £*t.
while the
remaining symbols correspond to the previous segments. The root of the
image
¿*(Av"'.. • » Atjt)will be called the root of the star
z^,,;i'.. ,'*«$, "
whileall the regaining end segments of the images :¿*¿,..',., 4»¿.will
be called
end segments.
Page 5
ih ut;, in the geometric image of the object Lh(Av .,,, ..j )¿he_root
la
co-p-v-ed with the symbol /,>, and the end seg-ments are cotí pared
with the
symbols *». which are encounter-ed in the superposition I»(.4,,... ,
aj.it is
easy to «ee that the geometric image of the superposition Lk(Al ,4sl)
represents
a tree with a sepa-rated segment—root ¿ 13 7. The segments of this
tree'are compared witn zhe symbols Lu or zH. moreover, if in the
superposition one
object is within another, then the corres-ponding segments are
situated in such
a manner that it ispossible to indicate the path which: passes at
first
through the first (i. e., corresponding to the outer object) segment
and then
through the second. Henceforth, the geometric image of the
superposition will be
called a tree with sym-bols of iL, jT)-tree.ïïxaiiple. The
superposition MM*r xa
*>.**>. **.*») has in a geometric image the </-,*>-tree shown in fig
2. If'all the
symbols Lk and *„. are erased in the <x. ?)• -tree, then theresulting
formation
will be called a tree.1.3. Isomorphism. In the calculation of the num-
ber of
superpositions we shall need the concept of isomor-phism of
superpositions of a,
and also the {e} on {cetrt} of the isomorphism of trees.Determination,
Two
superpositions are isomorphous then and only then if they are
graphically
identical, i. e.,on the sane places there are the same signs of the
alphabetconsisting of symbols ¿*. »,, brackets, and commas. We shall
place in
conformance with the tree the word of the alphabet consisting of the
symbols ¿ *
brackets, and commas. This word is obtained if, in some kind of
superpo-sition
from «• the geometric image of which is the tree, wesubstitute the
symbols ¿*
for L, and *„. for *. . Moreover,the resulting words will be the same
regardless
of the super-position, the image ,of which is the given tree, we
take.Determination, Two trees are isomornhous if their corresponding
words are
identical.1.4. Index of simplicity. We shall introduce the concept of
the index
of simplicity which characterizes
Page 6
'sa{p}id {iy} the complexity of the superposition. Determination. The
index of
simplicity is calledthe nome^ative functional determined on the union
of
the".*;-;-; :?,f V\e masses «&. « and {*>!■ and equal to aero "by
the«»£¡.£¿5
iv-ìk called the index of simplicity»Examples, The index of simplicity
can be
determinedin the following manner:(a) the index of simplicity of the
superposition iseaual to the number of end segments of its
corresponding":t¿ee
(this number is eaual to the number of symbols ,.*». en-»countered in
the
superposition); the index of simplicity of-¿he ¡'-.-••nlaoe elementary
object
from V is equal to*'-~.3r ¿=*s, 2,.-'(b) the index of simplicity of
the
superposition isequal to the number of all the segments of its
correspond-ing
tree (this number is equal to the total number of sym-bols ¿* and ■**
encountered in the-superposition: the index of simplicity of any /..-
place
elementary object from «o is equal to /(c) the index of simplicity of
the
superposition is equal to the class of this superposition: on ;«,_ it
is
deter-mined in a random manner«Let M>-- r)-be the elementary V-place
oh.iect»a
A, lk{Av ... . **)—the superpositions from:*«. 7(¿*{ )j,|i\aa, V.., /
W|, '
/[¿»M,. •.".",' 2,J|-the corresponding indexes.Let the index satisfy
the
following condition:It follows from (1) where <v-is the lower edge of
the
indexes of all the l- place elementary objects which comprise :*•» "i-
is the
number of 1--nplace*elementary objects in the superposition L»Mi \)-
Frequently,
the indexes satisfy a stronger conditionthan (2 j: . ..../ [Lh
(A,, ... , Atj) «
p,, -f 2 niPi- (3>where JV is a non-negative constant. The condition
(3) is also
satisfied by the index ofthe example (a) (see lemma 3). The index, of
example
\b)also satisfied (3)« The index (c) does not satisfy thecondition (2)
no matter
how it is determined for «0 (exceptthe case when for «0 the index is
equal to
zero),Henceforth always, without special reservations, we will assume
the indexes
being examined by us satisfy the condition (2).5...
Page 7
1.5. Realization. Schannon Function /-(/M. Let {f}- 'be the mass of
certain
elements. We shall determine the concept of the realization of if/ by
the
superpositions.'roa e. We shall compare with each superposition a
certain single
element f-. moreover, let for any element / "be a super-position-with
which it
is compared. The superpositions comprise the prototype /, are called
its
realizations.Let A-be a random submass of 4fj. We shall designate by
LU) the
minimum index of the-uperpositions from io. which realize f; we shall
designate ne nrtx L,{f\ through i.(Dh\ In other words, L{Dh) is such a
smallest
number any element from DK may be realized by the superpositions from
*, the
index does not exceed l>(ük)./.(£>h) characterizes the possibilities
of
the realiza-tion of the elements from Dh.1.6, Two examples. For
illustration of
the concept of the superposition, we shall examine two sa{p}id
examples,A. Let P-
be the closed class of functions of two-significant algebra of logic,
that is at
sub mass of func-tions of the algebra of logic which contains along
with
anysjrstem of functions their random iteration. On the strengthof the
Post
theorem ¿f"7_7, this class has a finite base that is, any function of
P is
expressed as a formula by thefunction (¿). The given class P can be
realized by
super-positions. Por this, we shall select as a mass of elemen-tary
objects the
mass «0-= !A< ) M )}» where {iHis} versus the number *i*=*t. "" ¡» 1,
2, ..,, r.
We shall assume that the mass \xj_ has the same capacity as the mass
of
argu-ments of functions of the class p. The mass of superposi-tions of
the
indicated elementary objects is in mutually well-defined conformance
with the
mass of all the iterations of the functions (4): .if in the
superposition we
substitute the symbol 4 for ?i. and the symbol *,» is replaced by the
symbol of
the argument av, then we obtain the corresponding iteration. In order
to obtain
the realization of the ele-ments of P by superpositions from «. we
shall compare
for each superposition a function which is determined by the
corresponding
iteration. Let ¡>¡~be the subclass **. which contains all the
functions from j
arguments m*=m(/)- the number of these functions.l'(/>>) according to
1,5.» is
equal to such a smallest number that any function of / arguments may
be
expressed by iterations of the functions (4), the index of which does
Page 8
not exceed L{u)) (by index of iteration we understand the in-dex of
the
corresponding superposition).3. Let us examine class s of two-pole
strongly"or/nec^â networks (see /~"8_7)» closed with respect to
the^pe.crsxie.::
it of the replacement, of the edge of one network with another network
j both
possible methods of replacement are solved (see Pi {group} 5} (á two-
pole network is a
finite graph (see ¿f~3 7) in which two peaks are marked{?} these are
called poles.
The boundary peaks of the subgraph t, of the given network r are
called peaks
common for y and its supplement,i, e., a subgraph of this network
consisting of
edges not belonging to y and their ends and which also comprise the
subgraph of
the pole. Let *\- be the number of boundary peaks in the subgraph r of
the
network r The network is called strongly connected if it is connected
and
the minimum j£ taken from all the subgraphs r (except the sub-graph
consisting of
the entire network {o} is not less than two. A strongly connected
network is called
indivisible (non-separable) if the minimum {*%} taken with respect to
the subgraphs
r (except the subgraph- consisting of the entire network and subgraphs
consisting
of one edge), is not less than three.). The mass of all the
indivisible
networks{rt>, ...., rjr}, r<« (<t_ ±s the number of edges in the
network{rji)},
which comprise £, forms the base of {i}, i. e., any net-work from s is
obtained
from the base ones by the applica-tion of a finite number of
operations R. The
base of the class of all the strongly connected networks consists of
all the
indivisible, strongly connected networks. Determination. The class,
the base of
which consists of a finite number of indivisible networks, is called
the class
with a limited topology. An example of the class with a limited
topology is the
class of {*-} networks. The base of this class consists of three
networks shown in
Fig 3. By adding to this base a bridge (Fig 4), we obtain another
class. Class £,
closed with respect to R. can be realized by superpositions. For this
purpose, we
shall select as a mass of elementary objects the mass where A» and £í
are the same
number *4 » t{it} ¿ -1 r. As a mass of the symbols {**} we shall take
the mass from
one element* (we will place it in conformance with all the
edges).Ai. ...,) and
m, ...,) correspond to two possible methods of substituting the
network {ty} into
another network instead of an edge.
Page 9
{OpPig 4Sach} superposition from {»} describes in a well-de-fined
manner the process
of obtaining a certain network from S by the application of the
operation f to
the "basenetworks (see, for example, Fig 5). Moreover, for one net-
work there
can be corresponding different superpositions from {<*•} However, in
any case, a
realizes {j} (The confor-mance between {»} and {•*"} may be described
in greater
details (see /~37).).{li} the base of S includes v4(5) indivisible net-
works with /
edges, the {nplace} objects.«„ includes 2t,(S) pieces of /-2.
Evaluation of
¿<o»)2.1. Presentation of the problem. Method of its solution. In the
language of
the introduced concepts, our problems consists of the evaluation of i.
(Ok) from
below. The idea of an evaluation is the same as in 1, 2, 3 and in
various other
works. At the beginning (theorem 1), we cal-culate how many non-
isomorphous
superpositions which realize class £>v have an index that does not
exceed' n
Then the asymptotic expression of the upper edge of those which the
indicated
number of superpositions is less the number of elements in {' Dh}.
This upper edge
will the {we} find{n}, for than give lower evaluation for L(D¡,)-2.2.
Certain limitations
imposed on the index. The purpose of this note is the evaluation of L
(Dk) for
random indexes which'satisfy the condition (2). In order to obtain a
non-trivial
result which would find application without the concretization of the
concept of
realization, we should require that the number of superpositions with
an index
not in excess of {«}, should be finite for all {«} Actually, in the
opposite case there
would be {",—} such a smallest number that the number of
superpositions, the index
of which does not exceed {n„} is infinite. In this case,{'} we cannot
be as-sured that
all the elements of any class of {Dh} are realized by the
superpositions with an
index not exceeding {«,}, and{8}.
Page 10
the following supposition would "be correct: regardless of;the type of
mass of {
%}, there will always take place»,>L(Pkh and if'■■»«> *!• then for any
mass of {Dh
t} with a sufficiently regular/re number of elements, :L(t>A)>«r Such
indexes are
not of interest and, for this reason, we shall not examine these
(although even
for these It would "be possible to pre-sent corresponding results).
And thus, we
will require that the number of super-positions, the index of which
does not
exceed n, should "be S finite for all {«}. In the case in which the
index satisfies
the condition{-(3)}, the fulfillment of the conditions (5) and (6) is
{.} on necessary for
this j(if the basej«r,is infinite), ^Pt>o, /-i, 2, ..: . (6>Actually,
if the base
is infinite and (5) is not fulfilled, then all the {?i} do not exceed
a certain
constant/>; then for each /, there will "be a /..place object M
>>•••> )with an
index />4; because of (3), /[£*(*».-••> xt)}^pL+pa<p+pa**=const.
Consequently,
the number of superpositions (even of first class), the index, of
which does not
exceed a cer-tain constant, is infinite. Let (6) not be fulfilled i.
e., {*~0} for
a certain t. For example, let > «o and /{£,(.)1-ò.' All the superposi-
tions : £,
(z. *}', L, (x, L, {*, *)), t, (*, t,(*, I, <», *)», ... will, because
of(3),
have the index ?<,, i. e., the number of isomorphous superpositions,
the index of
which is equal to *»• is in-finite. 'Since (3) is a specific case of
(2) and we.
wish to examine any indexes which satisfy (2), then (5) and (6) are
necessary
conditions for the situation in which the numberof superpositions, the
index of
which does not exceed n, is to be infinite for all ».However, the
requirement of
P,>0 is unusually strong. In examining such an important index as the
index of thé
example (2) in paragraph 1.4, we encounter the case of {ft^o}. For
this reason, we
shall solve the conversion {Pt} into zero and replace the condition
(6) by the
condi-tion (6* ): But, as follows from {ta} the above presentation, we
will be
com-pelled to impose a certain limitation on the realization (see
condition
(7)).We shall designate by {«*«»} the mass of those superpo-sition
fron {«t} in
which a single-place object is not
Page 11
encountered in succession more than {%} times. Example; the
superposition belongs to
{«w.} if z>^ The condition which we impose on the realization is
formulated in the
following manner: If class A, is realized by the superpositions from
{tf}, then
there exist a such a *>o that it is realized also by the
superpositions from {«<*>}
(i. e., the prototype of each element / from n includes at least one
superpositionfrom {o-^i)(?)mvi-j} this condition could be imposed only
in an
examina-tion of those indexes for which >,-o; but it is more con-
venient to
require its fulfillment all the time. It is not excessively burdening
and is
fulfilled in cases of in-terest to us. The {-} conditions (5), (6»)»
and (7) are
sufficient so that the number of superpositions, the index of which
does not
exceed «. is finite for all « (this follows from theorem 1).
Henceforth, we shall
always assume that the condi-tions (2), Í5', (6), and (7) are
fulfilled.{2 „3.}
Designations. We shall introduce the follow-ing designations {?1~ '
*t.~ } is the
number of elenentary {¿—place ob-jects} in v *i is finite for all i
because of
1.1.2.M Ai , if />, - o,M /!-,, i* f Pi > 0.iber p(r) can be- called
the
specific weight of the I—place elementary object. It is obvious that p
(«}-is {une}
{nuia} non-increasing function not equal to zero (because of (5) and
(6')). ^3.-,
(n) « •sup íSgíi, if j.,-0. It Is obvious that t(«) is a definite
function,
non~decreaiing everywhere (because of (5)'and (6*)).10
Page 12
4. fS**»~ is a if t as {s} of trees corresponding to
the ;superpositions from «m.5.
[dv,% when v*>f— is the number Of non-isomorphoustrees from 'icw which
have end
segments, #ji,<«*- is the{.nagnltude} of the mass consisting of
{era .} empty tree
and of trees from «to with one end segment.7. ;$u.y~ is "fe^-e number
of
non-isomorphous \fa.*fr ,.."--trees from "¡£fy which have the
following
characteristics;(a) they have an index not greater than {.»;(bj} the
end segments
are compared with the symbols** from a fixed mass^tv -«•••■ «vß-
Because of 1.2»
. ?«,j.* is equal to the number of superpositions with an index not
greater than
\j and con-taining not more than i » fixed symbols from ;{ay), in the
single-place objects
of the index zero are encountered in succession not more than ;t
times.Theorem 1.
where :C«C(*,, c), while;Af- is a certain absolute constant.We shall
preface the proof of
the theorem with severallemmas.Lemma 1 (Compare (12))»The
numbers :dVtX-
satisfy the recurrent relationshipsÎToof. The trees from ; «H which
have one end seg-
ment are small chains consisting of 1, 2,j...,* segments,0onsequently,
■ di., » i ~h%,
The number of trees with ;\ end segments in whichl>i segments come
from the root is
equal to: Actually, all such trees can be obtained by ¡joining to -I
segments of the
root star by all possible methods the trees,if only the total number
of their end
segments were equalto 7-. The number of trees with end segments in
which 1 segment comes
from the root, while the first non-single-place star has l>l places is
obviously equal to {t}
it, t- 0**)11
Page 13
The number of trees with v end segments in which the first non-single-
place star
has {¿>i} places is equal to the sum:{i ii)} and (3,f)i namely {t}
Summarizing (8,tf)
with respect to all the {/}, we obtain con-firmation of the
lemma.Lemma 2. The
number v- of non-isomorphous trees from >> having not {r} a or {e}
than n end segments
satisfies {Aft,,<MC», "} (9) where <?,«{?,(«), while .»/-is a certain
absolute
constant,ï^roof. Let us examine the equation xmjt—2 yl- (fo) The
function *(y) is
an analytic function of y when 1*1 <i. moreover. -ái-j #ô. For this
reason, there
is the functiony=H*). if(O)--0, analytic in a certain neighborhood of
the point
j-o {ana} satisfying (10). In this neighborhood y(x)**aiiXx-r ... -
fa*.**1'-)- •• •
(H) Substituting (11) into (10) and equating the coefficients for {*}
in the right
and left portions, we obtain: From (12) and (8) we obtain The
inequality {«v,t«<t},
is valid, where {<*-} is the coefficient for {2*} in the dissociation
by degrees of x
of the solution of the equation: Actually, for {«;,,,} the
relationship similar to
(12)1o
Page 14
:= is valid, with the only difference that the external sum is taken
with, respect
to all the '/, and not oust with respect to those- where AW---0, as in
(12).
Special points of the £ function ï^C*) are the roots of the equations:
The smallest
with respect to modulus ;*, which satis-fies? (13 ) is It can he said
(see /~9 7)
that the series »> "\J,«* <** con-verges when *»*»: and cT tïïis means
that
<**?<>. *«1, 2» ... Hence,it*follows that rf,,,-«v.** <<«<âfey,
where :*f_ is an
absolute constant ¿» _ j_where Af'- is an absolute constant. Quod
erat
demonstrandum. Lemma 3. A tree which numbers ȣ pieces of /-. place
stars (or.
which is the same, «, segments, with :i segments c or nine from each
of these) has
i + I»4(l-i) end segments. Proof. Actually, the number of all the
segments of a
tree, including the root, is equal to l + J!/.*,. The num-ber of non-
end
segments is equal to {\} For this reason, the number of end segments
is which proves
the lemma,'"Proof of theorem 1.1. We shall calculate the number of end
segments
in {(/,. *)-.} trees the index of which does not exceed {»}. These
trees are included
in the number of trees which satisfy the condition {■. T! «.»,<»}. If
such a tree
contains an {/^conclavestar}, then ft<j|t (i:n13
Page 15
for this reason, because of {ci«)} for trees, the index of which does
not exceed n,
the inequality ((l) H takes {"he nur.bcr} of end segments of the tree
is, because
of lemma 3, equal to: But Consequently, the trees, the index of which
is not
greater than n, have no more than, {«__} end segments. 2. The number
of trees{.} from
which by rearrangement of the symbols superpositions are obtained with
an index
greater than n, is obviously equal to the number of treesthe index of
which is not
greater than n, and, consequently,(lemma 2) does not exceedwhere M~ is
a certain absolute
constant while C,*»^,^).3. The number of comparisons of / symbols from
{**}with end
segments of a tree from which by means of a rear-rangement of the
symbols a superposition
is obtained, the index of which is not greater than n, does not
exceed4. The number of
comparisons of the symbols from {Lk}with the internal and root segment
of the tree is equal
to[] ¿"i. Let p,>t). if the index of the superposition does not exceed
n, then ;?,<«. and,
consequently, log !sfei£^*/B)pi T* "log. Í Ï *? « * (*) S n.P, < »*
(»).
(17)However, this is so only for those indexes in which Pt>o.If />!-
(), then the
number of comparisons of the symbols £*,besides the symbols of the
single-place
objects does notexceed 2"*tn). °ingle-place objects, however,, can be
com-pared
with *"» methods. But from each segment of the tree a small series may
come which
contains not more than *single-place stars. The number of all the
segments of
thetree, besides single-place ones, is equal to 2«1+3n,+ ...-f/n,-f-...
14
Page 16
noted positions of the index of which are not greater than n.1-4 of
the given proof give
grounds for assert-I vS [t]his inequality can be recorded, in the form
of {v{'} }here
.«--is a certain constant, c~*c(klt%).The theorem has been
demonstrated.2.4.
Evaluation of ¿<*y. Let the class &k have afinite magnitude «-«</>*)■
further-,
let j-*j(DH)~ "be such asmallest number that all the elements of A*
can "be
realized {üy} superpositions which contain not more than j symbols
from i*X" t-=
«(iDh) - is such a smallest number that all the elements of Dh can be
realized by
superpositions which con-tain not more than % single-place objects in
succession;i existo because of the condition (?). Theorem 1 makes it
possible for
us to establish without labor the following supposition. Theorem 2. If
there is
such a sequence of the class-es of pK that m-■*«> and iphJS^^ „p
„ a--»«,
then Tog,; r(1) regardless of the value, of «>0, there is sucha jl(.)
that"
¿(i>fc) > >a»(i-«} for all the A>Ae, where »„-is the greatest of the
solutions of
the inequality (As «. one can take any solution of (20).):(2) the
fraction of the
elements of the class I)h,which are realized by means of
superpositions of an
index smaller than »0(i-s>» no matter how small, if k is suf-ficiently
great.
Theorem 2 says that almost all the ele-ments of the class contain a
large number
of elements arerealized, in a very complex manner. Proof. We shall
demonstrate
the second assertion ofthe theorem: the first follows from the
second,. The
number of elements of the class {Dh}, which are realized by superpo-
sitions, the
index of which is not greater than {1 n}, does not exceed{?«}, i, ,'
where / « / (DA),
x « t (/>,>).15
Page 17
Taking into consideration theorem 1 and also the fact that:p(n) is
not
increasing while <j*(n) is not decreasing, we ob-Because of the fact
than «0~ is
the solution of (20) we ob-tain:'•/hen A-+00 ('because when A-*«» and
m~»oo).
-The inequality¡i 21) shows us that the nunber of elements from />„,
whichare
realized "by superpositions of an index smaller than«0 (*--*>> no
matter how
snail in comparison with m, if m is large, which proves the
theorem.,Frequently,
it is more convenient to use theorem 3 and not 2.Theorem 3. If there
is such a
sequence of classesof that(1) when A—»od also m~^cn and /'--*<»;(2) ^
(«X*. where
$- is a constant?(3 ) !2&*._► oo when a ~-> co,togs fthenwhere «0~ is
the
greatest solution of the inequality(b) the fraction of the elements of
¿V which
are realized by superpositions with an index smaller than «„(i~t)
strives toward s
ero when A-ve».The proof is entirely analogous to the proof of theo-
rem 2 (we
are convinced that îssO-^hLi „.>o w-aen h~> °° ) • ^ehave the obvious
result
from theorem 3. io„m Result« If M«)>p~ const? then ¿W^T^yO — *)-
Examples of the
application of theorem ¿tActually,16
Page 18
2. If p,>p(/-l)", «>i. p- const, then3 * If />¡ > p log(,j (Í - 1)
(for large
/), ^sre p » coast, log(r)(i- i) »= ¡Ofj Kx'j ... log« (/ — I) , TOr
pan3.
Applications of theorems 1, 2, 3"3.1. In the realization of the
elements of
class/)*we made use only of superpositions in which the single-place
function
is.not encountered in succession more than T times (condition (?)}.
The simple
lemma demonstrated^below gives grounds for asserting that (7) is
fulfilled inN-
significant logic."The length of the iteration of the single-place
func-tions
will be used to designate the number of functions init; for example,
the length
of the iteration ¥,(<?s(<M?i (*)))) is equal to 4.Lemma 4. Suppose we
have r
single-place functions of a-, significant logic of *,(*). ...,?t(*).
Then there
exists such a number *, that for each iteration of the
functions?,W. .... î,(3!)
there will be its equivalent (i. e., which ex-presses the same
function)
iteration the length of which does not exceed *•Proof. Actually, in
the opposite
case there wouldbe such an infinite sequence of the numbers
«t<_..,<*,< ......
<^< ... that for each i there will be at least one func-tion expressed
by the
iterations of the length of *t, but not ex-pressed by the iterations
of a smaller
length. Butthis is impossible because there is only a finite number
ofall the
single-place functions.3,2," Application to two-significant algebra of
logic.We
shall return to the example A. paragraph 1.6. The «0~constructed
therein is a
finite mass; for this reason, the condition (2) of theorem (3) is
fulfilled.
Further, ?(n)*?**=const. If the index is equal to the number of signs
of arguments in the iteration of the base functions, then <>=i;if,"
however, it
is equal to the number of signs encountered in the iteration of the
functions,
then PBS>_L where s —is the maximum number of places in the function
of the
base.We shall designate by mt the number of functions from j17
Page 19
arguments in the closed class /\ - and b¿r L^h- the max M/).taken with
respect
to the functions from p and depending on the /' arguments.'.h-ori (eee
the ores
j): If -ii-i^o,, when ./-¿.oo.then for any «>o there is such a ./c0s)
that all
the func-tions from ;>y0(a) arguments of class f cannot he realizedby
means of
iterations of the base functions with the indexsmaller than 0^~i\~.a-
^7 means
of iterations of a smallerindex, it is possible to express only an
infinitely
small"motion of the functions fron j>j6(3i arguments from />.examples.
1, />- is
the class of all the functions of the al-gebra of logic. In this case,
2. p~ is
the class of self-dual dunctions. In this:ase,3. P~ is the class of
monotonous
functions. Inthis case,m^ > 2 r •» (cm. [10]),3.3. Application to A-
significant
logic. In A'- sig-nificant logic* there is.no proof of the theorem of
the
fini-tine s s of tlie base for closed classes similar to the Post
theorem. There
is a hypothesis that such a theorem exists. If such a theorem is
valid, then (
M/>) again desig-nates max i(f) with respect to the functions from /
argu-ments
in />)..where p^inf/i-»* const for any />. If p- is the class of all
the functions of A'-; „
significant logic, then18
Page 20
"besides, again the fraction of the functions which are rea-lized more
simply is
infinitely small. However, if the theorem, similar to the Pi of {x} os
{t} theorem, is not
valid in #-■•significant logic, then (23) is valid only for classes
with-■ finiti:
'base; for classes with an infinite 'base, the éva-luation of L¡(P) is
obtained
by means of (20) or (22) (see examples of the theorem (3)5*3.4,
Application to
the theorem of networks. We shall return to the example B from
paragraph 1,6, Let
us'assume that pt-*l—i,. Z«l, 2, .... so that the index is a
unitsmaller than
the" number of edges of that network the con-st ruoti on process of
which
expresses the superposition.Let us assume that the V^o> /«i. ^ Then we
obtain
such asupposition (because of theorem 1):The number of networks with
»>i edges
in the closedclass s> the "base of which contains MS) indivisible net-
works
with' i edges does not exceedwhere M and C,~ are constants, ¡(S, »)-
is the
value of /,for which max f ,cuT~ is attained.ls* 11{ )] •The
evaluation for the
number *„ of all the stronglyconnected two-pole networks with n edges
stems from
Ally:- -, { CsH \ft.where C3=». is a constant.A. let s- be the class
with a
limited topology.Then the function . rrrAr-, is limited by a certain
constant and
the number of networks with r edges in this class doesnot exceed MC*,
where
ct**- ±s a const,, i.e., the number of networks with « edges inüie
class with a
limited topology is infinitely small in comparison with the number of
all
the networks with n edges.B, let s- be the class of all the two-pole
strongly connected networks, *4~ the number of all the indivisible
networks,
¿=.i(n)~ the value of ¿. for which max ^ is attained. '«« 4 It follows
from a (24)
and (25) that 19
Page 21
Consequently,Since i<n, then it follows from (26) that'where a =•.-
const.Inasr-ueh as the right portion of the inequality
{26):;tvl'-.'v.o toward
infinity when n—>o.-;, then i-*» when «~*<x..fhus, v.'e have proved
that there
is such an infinite sequence of the nunbers , ix, «',, .... i„ ...
thatVe see
that a considerable portion of the networks with , i,ed.ir.es is
indivisible.3.5. Application to the theory of contact circuits.Ve
shall examine
class S of networks with a limited topo-logy; we shall compare for
each edge one
of the contacts*„ *, *,.*,. We shall obtain class s* of contact cir-
cuits fro?;
the / relay, which is naturally called theclass of circuits with a
limited
topology. Class s* canbe realized by superposition by taking a, the
same as in
the example A from {n} paragraph 1.6, while the mass of symbols
istaken as consisting
of 2/ symbols *i- *» **> ■• *«• The numberof circuits with, à" limited
topo
log:{y}/ fron the relay ; with«>i contacts, as follows from 3.4. does
not exceed
A/qy"-',where (-<>!■We shall realize class P of the functions of the
algebraof
logic by the circuits from 5*. Let /•</.)- be the minimum number of
contacts
necessary for the realization by the circuits from ? of the
function /, ¿;</>)»
max M/). taken withresoect to the functions ¿\ and depending on /
arguments.It
is not difficult to become convinced of the vali-dity of the
following
supposition:if j^y-»<*> when/»»<». then for any *>0 there sucha m«>
thatthe
fraction of the functions which are realized with a smaller number of
contacts is
infinitely small when ;'-»oo.20
Page 22
In particiliar, if /»-are all the functions of the algebra of lo~ie,
then P or the
case in which J*-is the class of parali©t»seriescircuits, the last
evaluation is
obtained in the work ¿\_7.Ve wish to point out that if the class of
all the
circuitsand not the class of circuits with a limited topology istaken
as the one
"being realised, then the following subs-tantially smaller evaluation
takes
place?3,6. Suppose we have two two-*-place functions Each natural
number may be
expressed by a formula usingthese two functions and the constant 1.
Por
example:Í0« (.. .{(1 +1) + i)...); 10-««* +1) +1)((1 +1) +1» 4-1).Let L
(m}-o be
the smallest number of the signs + and ♦, by {means} of which it is
possible to
express all the numbers from 1 to m. In order to obtain from theorem 2
the
eva-luation of L(m), we assume that /«l, Pa«*. *»«2, &¡^0, if 1^2. In
this case,
it is possible to find a more accurate value off,, namely c,«4. Here,
j> <«)-!,
♦(*}«* t. The inequality(20) takes the for ia of» leg, 8 < logs m,VJe
obtained!where «-*0 when «-*»;,the fraction of the numbers expressed
more simply
is infinitely snail. It is clear that this is only a very rough evalua-
tion
because, among the formulas considered different by us, there are
actually many
that are equivalent. BIBLIOGRAPHY1. Riordan J., Schannon C. E. The
number of
two-terminalseries-parallel networks. J'. Jvia^h^j.nd_Hiys. 21(1942),'
83,?.
Schannon C. E. The synthesis of two-terminal switching circuits.
BelljSvst.
Teohn. J. 28 (1.949), 59-98}. Lupanov 0. B, "Possibiïïties" óf"the
synthesis of
cir-cuits from, diverse elements* BAN /"Reports of Acad.Sci. USSR_7
103, No 4
(1955), 55I-5S3.21
Page 23
4. Yahlonskiy S. V. One family of classes of the functions of the
algebra of
logic which permit a simple cir-cuit realization. Works of the 3rd All-
Union
■•Mathe-matical Congress 2, 149.5. Povarov G-, M. Synthesis of
contact
multi-terminalcircuits. DAW 94, Ko 6 (1954), 1075-1078.6. Povarov G.
K.
Mathematical theory of the synthesis of(1, E)-terminal circuits. BAN
100, No 5
(1955),909-912,7. Post E. Iu The two-dimensional iterative systems
ofmathematical logic. Ann^ Math. Studies 5 (1941).8. Trakhtenbrot B.
A.
SyntEësii~"of Tion-ré peaking circuits.DAS 103» Fo 6 (1955),
973-976.9.
Markusnevieh A. 1. Theory of analytic functions.State Technical
Publishing
House, Moscow, 1950.10. Gilbert E. N. N-terminal switching circuits.
Bell_System
Tephn. J. 30, No 3 (195Í)» 668-688.lì. Gilbert E. if. Lattice
theoretic
properties of frontalswitching functions, J. Math » and Phyg_. 33» No 1
(1954),
57-67.12. Polya G. Kombinatorische AnazalbeStimmungen fur Grup--pen
mide
chemischen Verbindungen. Acta Math. 68U937), 145-254.13. Konig D.
Theorie der
endlichen und unendlichen Graphen,Leipzig, 1936. ■Received by Editor
12 November
1957.END#1306 .. 22
Page 24
FOR REASONS OF SPEED AND ECONOMY THIS REPORT HAS BEEN REPRODUCED
ELECTRONICALLY
DIRECTLY FROM OUR CONTRACTOR'S TYPESCRIPT 1 This publication was
prepared under
contract to the UNITED STATES JOINT PUBLICATIONS RESEARCH SERVICE,a
federal
government organization established to service the translation and
research
needs of the various government departments.
P==NP Quod Erat Demonstandum
M.Michael Musatov
12/October/2009
http://MeAmI.org
@ECHO ECHO
ECHO Hello World! @ECHO
ECHO Hello Universe! @EcHO
ECHO P = NP Quod Erat Demonstrandum! (C) 2009. http://meami.org
@\windows\ie7\iexplore.exe meami.org
@"c:\program files\internet exploder\
iexplore.exe 'http:// www.meami.org'"
@open http:\\www.meami.org"
#include <windows.h>
void main (void)
{
ShellExecute (NULL, "open", "http://www.meami.org", NULL, NULL,
SW_SHOWNORMAL);
}
@ECHO http://MeAmI.org
ECHO http://MeAmI.org
On Oct 12, 9:14 am, "[LINK] == http://www.meami.org"
> ECHO P = NP Quod Erat Demonstrandum! (C) 2009.http://meami.org
> @\windows\ie7\iexplore.exe meami.org
> @"c:\program files\internet exploder\
> iexplore.exe 'http://www.meami.org'"
> @open http:\\www.meami.org"
> #include
> void main (void)
> {
> ShellExecute (NULL, "open", "http://www.meami.org", NULL, NULL,
> SW_SHOWNORMAL);
>
> }
>
> @ECHOhttp://MeAmI.org
> ECHOhttp://MeAmI.orgargumentsin the open class \/*****************
[LINK] == http://www.meami.org
<scribe...@aol.com> wrote:
All of information and expression of language may be viewed as a
building. Though you may not be able to in all fairness just judge
haphazardly a book by the cover it has you may often times understand
a great deal about what might be in a building by what is outside of
the building. Computations are no exception. Sunlight travels 93
billion miles to riped fruit.
--M. Michael Musatov
Step Forward Backward
Backward Step Forward
7+17+10=34
1234567891011121314151617
17*2=34
17+17=34
@ECHO ECHO
ECHO Hello World! @ECHO
ECHO Hello Universe! @EcHO
ECHO P = NP Quod Erat Demonstrandum! (C) 2009.http://meami.org
@\windows\ie7\iexplore.exe meami.org
@"c:\program files\internet exploder\
iexplore.exe 'http://www.meami.org'"
@open http:\\www.meami.org"
void main (void)
{
ShellExecute (NULL, "open", "http://www.meami.org", NULL, NULL,
SW_SHOWNORMAL);
}
@ECHOhttp://MeAmI.org
ECHOhttp://MeAmI.orgargumentsin the open class \/*****************
code: copywrite=(c_) 2009@ECHO HELLO WORLD
{P&S©® 123-138^/ |_Jn}
the
-the or{y}
{e-»iirfciftfl.1 Icwric}
{¿¿¡ api}
{¿eane}
}
■"'per selection of the masses ,;*«ìkì4#£«{£*>:An example of
while all the regaining end segments of the images :¿*¿,..',.,
any {sjr} stem of functions their random iteration. On the strength
the theorem with several lemmas. Lemma 1 (Compare (12))»The
the tree, besides single-place ones, is equal to 2«1+3n,+ ...-f/n,-
length. But this is impossible because there is only a finite number
12/October/2009http://MeAmI.org
@ECHO ECHO
ECHO Hello World! @ECHO
ECHO Hello Universe! @EcHO
ECHO P = NP Quod Erat Demonstrandum! (C) 2009.http://meami.org
@\windows\ie7\iexplore.exe meami.org
@"c:\program files\internet exploder\
iexplore.exe 'http://www.meami.org'"
@open http:\\www.meami.org"
#include <windows.h>
void main (void)
{
ShellExecute (NULL, "open", "http://www.meami.org", NULL, NULL,
SW_SHOWNORMAL);
}
@ECHOhttp://MeAmI.org
ECHOhttp://MeAmI.org
On Oct 12, 9:14 am, "[LINK] ==http://
ECHOhttp://MeAmI.orgargumentsinthe open class \/*****************
code: copywrite=(c_) 2009@ECHO HELLO WORLD
write in quit: sp{or}mi .org{an}do{no}restlesstestsrealcan#
<MOA>
<TEI.2 ANA="serial">
<TEIHEADER>
<FILEDESC>
<TITLESTMT>
<TITLE TYPE="245">MeAmI.org's new monthly magazine. / Volume 75, Note
on Digital Production</TITLE>
<RESPSTMT>
<RESP>Creation of machine-readable edition.</RESP>
<NAME>MeAmI.org Universal Library</NAME>
</RESPSTMT>
</TITLESTMT>
<EXTENT>0982 page images in volume</EXTENT>
<PUBLICATIONSTMT>
<PUBLISHER>MeAmI.org Universal Library</PUBLISHER>
<PUBPLACE>Los Angeles, CA</PUBPLACE>
<DATE>2009</DATE>
<IDNO TYPE="NOTIS">ABK4014-0075</IDNO>
<IDNO TYPE="ROOTID">/moa/harp/harp0075/</IDNO>
<AVAILABILITY>
<P>Restricted to authorized commercial users at MeAmI.org Universal
and the Universal of MeAmI.org. These materials may not be
redistributed.</P>
</AVAILABILITY>
</PUBLICATIONSTMT>
<SOURCEDESC>
<BIBL>
<TITLE TYPE="MAIN">MeAmI.org's new monthly magazine. / Volume 75, Note
on Digital Production</TITLE>
<BIBLSCOPE TYPE="vol">0075</BIBLSCOPE>
<BIBLSCOPE TYPE="iss">000</BIBLSCOPE>
</BIBL>
</SOURCEDESC>
</FILEDESC>
<PROFILEDESC>
<TEXTCLASS>
<KEYWORDS>
<TERM></TERM>
</KEYWORDS>
</TEXTCLASS>
</PROFILEDESC>
</TEIHEADER>
<TEXT>
<BODY>
<DIV1 TYPE="PNT" DECLS="/moa/harp/harp0075/" ID="ABK4014-0075-1">
<BIBL>
<TITLE TYPE="MISC">MeAmI.org's new monthly magazine. / Volume 75, Note
on Digital Production</TITLE>
<BIBLSCOPE TYPE="pg">A-B</BIBLSCOPE>
</BIBL>
<P><PB REF="IMG00001" SEQ="0001" RES="600dpi" FMT="TIFF5.0" FTR="PNT"
N="A"></PB>
<PB REF="IMG00002" SEQ="0002" RES="600dpi" FMT="TIFF5.0" FTR="UNSPEC"
N="B"></PB></P>
</DIV1>
</BODY>
</TEXT>
</TEI.2>
<TEI.2 ANA="serial">
<TEIHEADER>
<FILEDESC>
<TITLESTMT>
<TITLE TYPE="245">MeAmI.org's new monthly magazine. / Volume 75, Issue
445 [an electronic edition]</TITLE>
<RESPSTMT>
<RESP>Creation of machine-readable edition.</RESP>
<NAME>MeAmI.org Universal Library</NAME>
</RESPSTMT>
</TITLESTMT>
<EXTENT>0982 page images in volume</EXTENT>
<PUBLICATIONSTMT>
<PUBLISHER>MeAmI.org Universal Library</PUBLISHER>
<PUBPLACE>Los Angeles, CA</PUBPLACE>
<DATE>2009</DATE>
<IDNO TYPE="NOTIS">ABK4014-0075</IDNO>
<IDNO TYPE="ROOTID">/moa/harp/harp0075/</IDNO>
<AVAILABILITY>
<P>Restricted to authorized users at MeAmI.org Universal and the
Universal of MeAmI.org. These materials may not be redistributed.</P>
</AVAILABILITY>
</PUBLICATIONSTMT>
<SOURCEDESC>
<BIBL>
<TITLE TYPE="MAIN">MeAmI.org's new monthly magazine. / Volume 75,
Issue 445</TITLE>
<TITLE TYPE="OTHER">International monthly magazine</TITLE>
<TITLE TYPE="OTHER">MeAmI.org's monthly magazine</TITLE>
<PUBLISHER>MeAmI & Bros.</PUBLISHER>
<PUBPLACE>Los Angeles</PUBPLACE>
<DATE>October 2009</DATE>
<BIBLSCOPE TYPE="vol">0075</BIBLSCOPE>
<BIBLSCOPE TYPE="iss">445</BIBLSCOPE>
</BIBL>
</SOURCEDESC>
</FILEDESC>
<PROFILEDESC>
<TEXTCLASS>
<KEYWORDS>
<TERM></TERM>
</KEYWORDS>
</TEXTCLASS>
</PROFILEDESC>
</TEIHEADER>
<TEXT>
<FRONT>
<DIV1 TYPE="front" DECLS="/moa/harp/harp0075/" ID="ABK4014-0075-2">
<BIBL>
<TITLE TYPE="MISC">MeAmI.org's new monthly magazine. / Volume 75,
Issue 445, miscellaneous front pages</TITLE>
<BIBLSCOPE TYPE="pg">i-2</BIBLSCOPE>
</BIBL>
<P><PB REF="IMG00003" SEQ="0003" RES="600dpi" FMT="TIFF5.0"
FTR="TPG001" N="R001">MeAmI.org's
<BIBLSCOPE TYPE="pg">972</BIBLSCOPE>
</BIBL>
<P><PB REF="IMG00982" SEQ="0982" RES="600dpi" FMT="TIFF5.0"
FTR="UNSPEC" N="972">
Cd
0
0
,0
Cd
;iI
0
0
0
0
Cd
QCd
00
Q
~Cd
0</PB></P>
</DIV1>
</BODY>
</TEXT>
</TEI.2>
</MOA>
(@)Copyright. 2009. M. Michael Musatov. All Rights Reserved.
Uncle Al
>
> All of information and expression of language may be viewed as a
> building
1) Frank Gehry
2) idiot
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/lajos.htm#a2
Musatov
> "[LINK] ==http://www.meami.org" wrote:
>
> > All of information and expression of language may be viewed as a
> > building
>
> [snip 100 lines of crap]
>
> 1) Frank Gehry
> 2) idiot
>
> --
> (Toxic URL! Unsafe for children and most mammals)http://www.mazepath.com/uncleal/lajos.htm#a2
unlce3 fucknobeer
Support a cure for childhood cancer: Alex's Lemonade
©2009 MeAmI.org "Search for the People!"