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NATURES GENERAL LEDGER : THE GRAND DESIGN MODEL FOR A SIMULATED
UNIVERSE-A GIANT DIGITAL COMPUTER AT WORK
1DR K N PRASANNA KUMAR, 2PROF B S KIRANAGI AND 3 PROF C S BAGEWADI
ABSTRACT: Consciousness could be thought of as the problem to which propositions belong and
concomitantly correspond as they indicate particular responses ,signify instances of general solutions, with its
essential configurations, rational representations conferential extrinsicness, interfacial interference,
syncopated justices, heterogeneous variations testimonies,apodeictic knowledge of ideological
tergiversation,sauccesful reality,sleaty sciolisms,tiurated vaticinations,anchorite aperitif anamensial
alienisms and manifest subjective acts of resolution . Consciousness in its organization of singular points,
series and displacements, is doubly generative; it not only engenders the logical propositions with its
determinate dimensions but also its correlates. The equivocality, ambiguity, in the synchronicity of the
problem and proposition both in the sets and subsets of the ontological premises and logical boundaries,
error in perception arises in the field of consciousness. Far from indicating the subjective and provisional
state of empirical knowledge consciousness refers to an ideational objectivity or to a structure constitutive ofspace and time, the knowledge and the known, the proposition and its correlates. The question of question
in consciousness does not bear any resemblance to the proposition which subsumes it, but rather it determines
its own conditionalities and representationalitiesof and assigns them to its constituents in various
permutations and combinations, that are done with corporate signification, personalized manifestation,
individual denotation and organizational individuation. Consciousness is only the shadow of the problem
projected or rather constructed based on empirical propositions. It is the same illusion which does not allow
it to be reduced to any empirical thesis or antithesis for that matter. Retroactive movement of consciousness
based on morphemes, semitones and relational openness leads to disintegration of external relations and
dysfunctional fissures in the personality domains of resolvability are relativistic in the self determination of
the consciousness problem. Consciousness makes signification as the condition of truth and proposition as
the conditional truth; it is necessary that we should not vie the condition as the one who is conditioned, lestthe biases of internationality and subject object conflict arise. Witness consciousness is the best answer to the
problems that we face in science. Static genesis sets right the aham brahasmi (I AM Brahman) and from
Brahman we came problem. Consciousness thus is neutral but never the double of the propositions which
express it. Events have critical points like say liquids have, or water has. in all its pristine glory and
primordial mortification consciousness is just knowledge, expressed in bytes, visual field capacity is also
expressed. We make an explicit assumption that the storage is measured based on the number of bytes and
that ASCII is used. Further assumption in gratification deprivation is that gratification increases in arithmetic
progression, and deprivation in geometric progression. More you think, more you get angry. The still more
you think you go mad. Repetitive actions and thoughts which are themselves actions are assumed to be
recorded. by a hypotherticalneuron DNA. We thus record everything in the general ledger of the universe.
And lo! The grand design simulated by someone, with people like us with Tams, rajas (dynamism) and
sattva (the transcendental form of Tams and rajas) react. The height is the murder, mayhem calypso and
cataclysm. the depth is non reaction ability. With this we state that this universe is s grand design simulated
and we are really playing our roles to fit in a virtual drama.
INTRODUCTION:
We take in to considerations following parameters:
(1)
Consciousness(just the amount of bytes recorded and visual representations measured byInformation field capacity)
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(2) Perception (What we see-It is said by many people like Kant and Indian Brihadyaranyaka Sutra thatwhat you see is not what you see; what you do not see is not what you do not see; what you see is
what you do not see and what you do not see is what you see Here we assume that perception is
what we see. And note in the Model we are making a case for the augmented reality or dissipated
reality if the observer has consciousness, by which we mean what exactly is happening. If two
crime syndicates are fighting each other, you may only see a terrible traffic and do not see anything
else!)
(3) Gratification (we assume that it increases, the balance increases by arithmetic progression .The moreyou think, the same sentences form again and can be measured by ASCII numbersToo much
needless to say leads to paranoid schizophrenia. All actions are performed by people to achieve
gratification or deprivation, that includes sadists and masochists)
(4) Deprivation(Balance here increases by GP ;again ASCII is used)(5) Space(6) Time(7) Vacuum Energy(8) Quantum Field(9) Quantum Gravity(10)Environmental Coherence(11)Mass(12)Energy
CONSCIOUSNESS AND PERCEPTION MODULE NUMBERED ONE
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NOTATION :
: CATEGORY ONE OF PERCEPTION
: CATEGORY TWO OF PERCEPTION
: CATEGORY THREE OFPERCEPTION : CATEGORY ONE OF THE CONSCIOUSNESS : CATEGORY TWO OF THE CONSCIOUSNESS :CATEGORY THREE OF THE CONSCIOUSNESSSPACE AND TIME MODULE NUMBERED TWO:
=============================================================================
: CATEGORY ONE OFTIME : CATEGORY TWO OF TIME : CATEGORY THREE OF TIME :CATEGORY ONE OFSPACE : CATEGORY TWO OF SPACE : CATEGORY THREE OF SPACEGRATIFICATIONA AND DEPRIVATION(MOSTLY UNCONSERVATIVE HOLISTICALLY AND
INDIVIDUALLY! WORLD IS AN EXAMPLE) MODULE NUMBERED THREE:
=============================================================================
: CATEGORY ONE OF DEPRIVATION :CATEGORY TWO OF DEPRIVATION : CATEGORY THREE OF DEPRIVATION : CATEGORY ONE OF GRATIFICATION
:CATEGORY TWO OF GRATIFICATION
: CATEGORY THREE OF GRATIFICATION
MASS AND ENERGY:MODULE NUMBERED FOUR:
============================================================================
: CATEGORY ONE OF MATTER
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: CATEGORY TWO OFMATTER : CATEGORY THREE OF MATTER
:CATEGORY ONE OF ENERGY
:CATEGORY TWO OF ENERGY : CATEGORY THREE OF ENERGYVACUUM ENERGY AND QUANTUM FIELD:MODULE NUMBERED FIVE:
=============================================================================
: CATEGORY ONE OF QUANTUM FIELD : CATEGORY TWO OFQUANTUM FIELD :CATEGORY THREE OF QUANTUM FIELD :CATEGORY ONE OF VACUUM ENERGY :CATEGORY TWO OF VACUUM ENERGY :CATEGORY THREE OF VACUUM ENERGY
ENVIRONMENTAL COHERENCE AND QUANTUM GRAVITY:MODULE NUMBERED SIX:
=============================================================================
: CATEGORY ONE OFENVIRONMENTAL COHERENCE : CATEGORY TWO OF ENVIRONMENTAL COHERENCE : CATEGORY THREE OF ENVIRONMENTAL COHERENCE : CATEGORY ONE OF QUANTUM GRAVITY : CATEGORY TWO OF QUANTUM GRAVITY : CATEGORY THREE OF QUANTUM GRAVITY==============================================================================
= : , are Accentuation coefficients
,
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are Dissipation coefficientsThe differential system of this model is now (Module Numbered one)
CONSCIOUSNESS AND PERCEPTION MODULE NUMBERED ONE
[ ] [ ] [ ] [ ] [ ] [ ] First augmentation factor First detritions factorThe differential system of this model is now ( Module numbered two)
SPACE AND TIME MODULE NUMBERED TWO
[ ] [ ] [ ] [ ()] [ ()] [ ()]
First augmentation factor
( ) First detritions factorThe differential system of this model is now (Module numbered three)
GRATIFICATIONA AND DEPRIVATION(MOSTLY UNCONSERVATIVE HOLISTICALLY AND
INDIVIDUALLY! WORLD IS AN EXAMPLE) MODULE NUMBERED THREE
[ ] [ ] [ ]
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[ ] [ ] [ ] First augmentation factor First detritions factor
MASS AND ENERGY:MODULE NUMBERED FOUR:
The differential system of this model is now (Module numbered Four)
[ ] [ ] [ ] [ ()] [ ()] [ ()]
First augmentation factor
( ) First detritions factorThe differential system of this model is now (Module number five)
VACUUM ENERGY AND QUANTUM FIELD:MODULE NUMBERED FIVE
[ ] [ ]
[ ] [ ()] [ ()] [ ()]
First augmentation factor
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( ) First detritions factorThe differential system of this model is now (Module numbered Six)
ENVIRONMENTAL COHERENCE AND QUANTUM GRAVITY:MODULE NUMBERED SIX
[ ] [ ] [ ] [ ()] [ ()] [ ()] First augmentation factor ( ) First detritions factorHOLISTIC CONCATENATE SYTEMAL EQUATIONS HENCEFORTH REFERRED TOAS GLOBAL EQUATIONS
CONSCIOUSNESS AND PERCEPTION MODULE NUMBERED ONE
SPACE AND TIME MODULE NUMBERED TWO
GRATIFICATIONA AND DEPRIVATION(MOSTLY UNCONSERVATIVE HOLISTICALLY AND
INDIVIDUALLY! WORLD IS AN EXAMPLE) MODULE NUMBERED THREE
VACUUM ENERGY AND QUANTUM FIELD:MODULE NUMBERED FIVE
MASS AND ENERGY:MODULE NUMBERED FOUR
ENVIRONMENTAL COHERENCE AND QUANTUM GRAVITY:MODULE NUMBERED SIX
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Where
are first augmentation coefficients for category 1, 2 and 3
, , are second augmentation coefficient for category 1, 2 and 3 are third augmentation coefficient for category 1, 2 and 3
, , are fourth augmentation coefficient for category 1, 2 and 3 are fifth augmentation coefficient for category 1, 2 and 3 , , are sixth augmentation coefficient for category 1, 2 and 3
Where are first detrition coefficients for category 1, 2 and 3 are second detrition coefficients for category 1, 2 and 3 are third detrition coefficients for category 1, 2 and 3 are fourth detrition coefficients for category 1, 2 and 3 , , are fifth detrition coefficients for category 1, 2 and 3 , , are sixth detrition coefficients for category 1, 2 and 3
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Where are first augmentation coefficients for category 1, 2 and 3 , , are second augmentation coefficient for category 1, 2 and 3
are third augmentation coefficient for category 1, 2 and 3
are fourth augmentation coefficient for category 1, 2 and 3 , , are fifth augmentation coefficient for category 1, 2 and 3 , , are sixth augmentation coefficient for category 1, 2 and 3
, , are first detrition coefficients for category 1, 2 and 3 , are second detrition coefficients for category 1,2 and 3 are third detrition coefficients for category 1,2 and 3 are fourth detrition coefficients for category 1,2 and 3 , , are fifth detrition coefficients for category 1,2 and 3 , are sixth detrition coefficients for category 1,2 and 3
, , are first augmentation coefficients for category 1, 2 and 3
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, are second augmentation coefficients for category 1, 2 and 3 are third augmentation coefficients for category 1, 2 and 3
,
are fourth augmentation coefficients for category 1, 2 and
3
are fifth augmentation coefficients for category 1, 2 and 3 are sixth augmentation coefficients for category 1, 2 and 3
are first detrition coefficients for category 1, 2 and 3 , , are second detrition coefficients for category 1, 2 and 3
,
are third detrition coefficients for category 1,2 and 3
are fourth detrition coefficients for category 1, 2 and 3 are fifth detrition coefficients for category 1, 2 and 3 are sixth detrition coefficients for category 1, 2 and 3
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are fourth augmentation coefficients for category 1, 2,and 3 , are fifth augmentation coefficients for category 1, 2,and 3 , , are sixth augmentation coefficients for category 1, 2,and 3
, , ,
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are fourth augmentation coefficients for category 1,2, and 3
are fifth augmentation coefficients for category 1,2,and 3 are sixth augmentation coefficients for category 1,2, 3
are fourth detrition coefficients for category 1,2, and 3 are fifth detrition coefficients for category 1,2, and 3 , are sixth detrition coefficients for category 1,2, and 3
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- are fourth augmentation coefficients - fifth augmentation coefficients
,
sixth augmentation coefficients
are fourth detrition coefficients for category 1, 2, and 3 , are fifth detrition coefficients for category 1, 2, and 3 , are sixth detrition coefficients for category 1, 2, and 3
Where we suppose
(A) (B) The functions
are positive continuous increasing and bounded.
Definition of : (C) Definition of :
Where are positive constants and
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They satisfy Lipschitz condition:
With the Lipschitz condition, we place a restriction on the behavior of functions and and are points belonging to the interval[ ] . It is to be noted that is uniformly continuous. In the eventuality of thefact, that if then the function , the first augmentation coefficient WOULD beabsolutely continuous.
Definition of :(D) are positive constants
Definition of :(E) There exists two constants and which together
with and and the constants satisfy the inequalities
Where we suppose
(F) (G) The functions are positive continuous increasing and bounded.Definition of :
( )
(H) ( ) Definition of :Where are positive constants and They satisfy Lipschitz condition:
( )
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With the Lipschitz condition, we place a restriction on the behavior of functions and . and are points belonging to the interval [ ] . It is tobe noted that is uniformly continuous. In the eventuality of the fact, that if thenthe function
, the SECOND augmentation coefficient would be absolutely continuous.
Definition of :(I) are positive constants
Definition of :There exists two constants and which togetherwith and the constants
satisfy the inequalities
Where we suppose
(J) The functions are positive continuous increasing and bounded.Definition of : Definition of :Where
are positive constants and
They satisfy Lipschitz condition:
With the Lipschitz condition, we place a restriction on the behavior of functions and . And are points belonging to the interval [ ] . It is tobe noted that is uniformly continuous. In the eventuality of the fact, that if thenthe function , the THIRD augmentation coefficient, would be absolutely continuous.Definition of :
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(K) are positive constants
There exists two constants There exists two constants and which together with and the constants satisfy the inequalities
Where we suppose
(M) The functions are positive continuous increasing and bounded.Definition of :
( )
(N)
( ) Definition of :Where are positive constants and
They satisfy Lipschitz condition:
( )
With the Lipschitz condition, we place a restriction on the behavior of functions and . and are points belonging to the interval [ ] . It is tobe noted that is uniformly continuous. In the eventuality of the fact, that if thenthe function , the FOURTH augmentation coefficient WOULD be absolutely continuous.Definition of :
are positive constants
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Definition of :(Q) There exists two constants and which together with
and the constants
satisfy the inequalities
Where we suppose
(S) The functions are positive continuous increasing and bounded.Definition of
: ( )
(T) Definition of :Where are positive constants and They satisfy Lipschitz condition:
( ) With the Lipschitz condition, we place a restriction on the behavior of functions and . and are points belonging to the interval [ ] . It is tobe noted that
is uniformly continuous. In the eventuality of the fact, that if
then
the function , theFIFTH augmentation coefficient attributable would be absolutelycontinuous.Definition of :
are positive constants Definition of :
There exists two constants
and
which together with
and the constants satisfy the inequalities
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Where we suppose
(W) The functions are positive continuous increasing and bounded.
Definition of :
(X) ( ) Definition of :
Where are positive constants and They satisfy Lipschitz condition:
( )
With the Lipschitz condition, we place a restriction on the behavior of functions and . and are points belonging to the interval [ ] . It is tobe noted that is uniformly continuous. In the eventuality of the fact, that if thenthe function , the SIXTH augmentation coefficient would be absolutely continuous.Definition of : are positive constants
Definition of :There exists two constants and which together with and the constants satisfy the inequalities
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Theorem 1: if the conditions IN THE FOREGOING above are fulfilled, there exists a solution satisfying the
conditions
Definition of : ( ) , ,
Definition of ,
,
, , Definition of :
( )
,
, Definition of : ( ) , , Definition of : ( ) , , Proof: Consider operator defined on the space of sextuples of continuous functions which satisfy
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By
() (() ) ()
() (() ) () () (() ) () () (() ) () () (() ) ()
(
)
((
)
)
(
)
Where is the integrand that is integrated over an interval Proof:
Consider operator defined on the space of sextuples of continuous functions whichsatisfy
By
() (() ) () () (() ) () () (() ) ()
() (() ) ()
() (() ) () () (() ) () Where is the integrand that is integrated over an interval Proof:
Consider operator
defined on the space of sextuples of continuous functions
which
satisfy
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By
() (() ) () () (() ) ()
() (() ) () () (() ) () () (() ) () () (() ) () Where is the integrand that is integrated over an interval Consider operator defined on the space of sextuples of continuous functions whichsatisfy
By
() (() ) () () (() ) ()
()
(() ) ()
() (() ) () () (() ) () () (() ) () Where is the integrand that is integrated over an interval Consider operator defined on the space of sextuples of continuous functions whichsatisfy
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By
() (() ) () () (() ) ()
() (() ) ()
()
(() ) ()
() (() ) () () (() ) () Where is the integrand that is integrated over an interval Consider operator defined on the space of sextuples of continuous functions whichsatisfy
By
() (() ) ()
() (() ) ()
() (() ) () () (() ) () () (() ) () () (() ) () Where
is the integrand that is integrated over an interval
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(a) The operator maps the space of functions satisfying GLOBAL EQUATIONS into itself .Indeed itis obvious that
( ) From which it follows that
( )
is as defined in the statement of theorem 1Analogous inequalities hold also for
(b) The operator maps the space of functions satisfying GLOBAL EQUATIONS into itself .Indeed itis obvious that
( ) From which it follows that
(
)
Analogous inequalities hold also for (a) The operator maps the space of functions satisfying GLOBAL EQUATIONS into itself .Indeed it
is obvious that
( )
From which it follows that
( ) Analogous inequalities hold also for (b) The operator maps the space of functions satisfying GLOBAL EQUATIONS into itself .Indeed it
is obvious that ( )
From which it follows that
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( )
is as defined in the statement of theorem 1
(c) The operator maps the space of functions satisfying GLOBAL EQUATIONS into itself .Indeed itis obvious that ( )
From which it follows that
(
)
is as defined in the statement of theorem 1(d) The operator maps the space of functions satisfying GLOBAL EQUATIONS into itself .Indeed it
is obvious that
( )
From which it follows that
( )
is as defined in the statement of theorem 6Analogous inequalities hold also for
It is now sufficient to take and to choose large to have ( )
(
)
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In order that the operator transforms the space of sextuples of functions satisfying GLOBALEQUATIONS into itself
The operator is a contraction with respect to the metric( )( ) | | | |Indeed if we denote
Definition of :( )
It results
| | | | | | ( )| | ( ) ( ) Where represents integrand that is integrated over the interval From the hypotheses it follows
| | ( )( )And analogous inequalities for . Taking into account the hypothesis the result followsRemark 1: The fact that we supposed depending also on can be considered as notconformal with the reality, however we have put this hypothesis ,in order that we can postulate condition
necessary to prove the uniqueness of the solution bounded by respectively ofIf instead of proving the existence of the solution on
, we have to prove it only on a compact then it
suffices to consider that
depend only on
and respectively on
and hypothesis can replaced by a usual Lipschitz condition.Remark 2: There does not exist any where From 19 to 24 it results
{(())} () for Definition of ( )( ) ( ) :Remark 3: if is bounded, the same property have also . indeed if
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it follows ( ) and by integrating ( ) ( ) In the same way , one can obtain
( ) ( ) If is bounded, the same property follows for and respectively.
Remark 4: If bounded, from below, the same property holds for The proof isanalogous with the preceding one. An analogous property is true if is bounded from below.Remark 5: If is bounded from below and then
Definition of :Indeed let
be so that for
Then
which leads to If we take such that it results By taking now sufficiently small one sees that is unbounded.The same property holds for if We now state a more precise theorem about the behaviors at infinity of the solutions
It is now sufficient to take and to choose large to have
( )
( ) In order that the operator transforms the space of sextuples of functions satisfyingThe operator is a contraction with respect to the metric ( ) ( )
|
|
|
|
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Indeed if we denote
Definition of : ( ) It results
| | | | | | ( )| | ( ) ( ) Where represents integrand that is integrated over the interval From the hypotheses it follows
| | ( )( )And analogous inequalities for . Taking into account the hypothesis the result followsRemark 1: The fact that we supposed depending also on can be considered as notconformal with the reality, however we have put this hypothesis ,in order that we can postulate condition
necessary to prove the uniqueness of the solution bounded by respectively ofIf instead of proving the existence of the solution on
, we have to prove it only on a compact then it
suffices to consider that depend only on and respectively on and hypothesis can replaced by a usual Lipschitz condition.Remark 2: There does not exist any where From 19 to 24 it results
{(())} () for Definition of
(
)
(
) (
):
Remark 3: if is bounded, the same property have also . indeed if it follows ( ) and by integrating ( ) ( ) In the same way , one can obtain
( ) ( ) If is bounded, the same property follows for and respectively.
Remark 4: If bounded, from below, the same property holds for The proof is analogouswith the preceding one. An analogous property is true if is bounded from below.
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Remark 5: If is bounded from below and then Definition of :Indeed let
be so that for
Then
which leads to If we take such that it results By taking now sufficiently small one sees that is unbounded. Thesame property holds for if ( ) We now state a more precise theorem about the behaviors at infinity of the solutions
It is now sufficient to take and to choose large to have
( )
( )
In order that the operator transforms the space of sextuples of functions into itselfThe operator is a contraction with respect to the metric ( ) ( ) | | | |Indeed if we denote
Definition of :( ) ( )It results
| | | | | | ( )| | ( ) ( )
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Where represents integrand that is integrated over the interval From the hypotheses it follows
| |
( )( )And analogous inequalities for . Taking into account the hypothesis the result followsRemark 1: The fact that we supposed depending also on can be considered as notconformal with the reality, however we have put this hypothesis ,in order that we can postulate condition
necessary to prove the uniqueness of the solution bounded by respectively ofIf instead of proving the existence of the solution on , we have to prove it only on a compact then itsuffices to consider that depend only on and respectively on
and hypothesis can replaced by a usual Lipschitz condition.
Remark 2: There does not exist any where From 19 to 24 it results
{(())} () for Definition of ( )( ) ( ) :Remark 3: if
is bounded, the same property have also
. indeed if
it follows ( ) and by integrating ( ) ( ) In the same way , one can obtain
( ) ( ) If is bounded, the same property follows for and respectively.
Remark 4: If bounded, from below, the same property holds for The proof isanalogous with the preceding one. An analogous property is true if
is bounded from below.
Remark 5: If is bounded from below and ( ) then Definition of :Indeed let be so that for ( ) Then
which leads to
If we take
such that
it results
By taking now sufficiently small one sees that is unbounded.
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The same property holds for if ( ) We now state a more precise theorem about the behaviors at infinity of the solutions
It is now sufficient to take and to choose large to have ( )
(
)
In order that the operator transforms the space of sextuples of functions satisfying IN to itselfThe operator is a contraction with respect to the metric ( ) ( ) | | | |Indeed if we denote
Definition of : ( ) It results
| | | | | | ( )| |
( ) ( ) Where represents integrand that is integrated over the interval From the hypotheses it follows
| | ( )( )And analogous inequalities for . Taking into account the hypothesis the result followsRemark 1: The fact that we supposed
depending also on
can be considered as not
conformal with the reality, however we have put this hypothesis ,in order that we can postulate condition
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necessary to prove the uniqueness of the solution bounded by respectively ofIf instead of proving the existence of the solution on
, we have to prove it only on a compact then it
suffices to consider that depend only on and respectively on and hypothesis can replaced by a usual Lipschitz condition.Remark 2: There does not exist any where From 19 to 24 it results
{(())} () for Definition of
(
)
(
) (
):
Remark 3: if is bounded, the same property have also . indeed if it follows ( ) and by integrating ( ) ( ) In the same way , one can obtain
( ) ( ) If
is bounded, the same property follows for
and
respectively.
Remark 4: If bounded, from below, the same property holds for The proof isanalogous with the preceding one. An analogous property is true if is bounded from below.Remark 5: If is bounded from below and then Definition of :Indeed let be so that for
Then which leads to If we take such that it results By taking now sufficiently small one sees that is unbounded.The same property holds for if ( ) We now state a more precise theorem about the behaviors at infinity of the solutions ANALOGOUS
inequalities hold also for
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It is now sufficient to take and to choose
large to have
( )
( )
In order that the operator transforms the space of sextuples of functions into itselfThe operator is a contraction with respect to the metric ( ) ( ) | | | |Indeed if we denote
Definition of : ( ) ( )It results
| | | | | | ( )| | ( ) ( ) Where
represents integrand that is integrated over the interval
From the hypotheses it follows
| | ( )( )And analogous inequalities for . Taking into account the hypothesis (35,35,36) the result followsRemark 1: The fact that we supposed depending also on can be considered as notconformal with the reality, however we have put this hypothesis ,in order that we can postulate condition
necessary to prove the uniqueness of the solution bounded by
respectively of
If instead of proving the existence of the solution on , we have to prove it only on a compact then it
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suffices to consider that depend only on and respectively on and hypothesis can replaced by a usual Lipschitz condition.Remark 2: There does not exist any
where
From GLOBAL EQUATIONS it results
{(())} () for Definition of ( )( ) ( ) :Remark 3: if is bounded, the same property have also . indeed if
it follows
(
)
and by integrating
( ) ( ) In the same way , one can obtain
( ) ( ) If is bounded, the same property follows for and respectively.
Remark 4: If bounded, from below, the same property holds for The proof isanalogous with the preceding one. An analogous property is true if is bounded from below.Remark 5: If is bounded from below and then Definition of :Indeed let be so that for
Then
which leads to If we take such that it results By taking now sufficiently small one sees that is unbounded.The same property holds for if ( ) We now state a more precise theorem about the behaviors at infinity of the solutions
Analogous inequalities hold also for
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It is now sufficient to take and to choose
large to have ( ) ( )
In order that the operator transforms the space of sextuples of functions into itselfThe operator is a contraction with respect to the metric ( ) ( ) | | | |Indeed if we denote
Definition of : ( ) ( )It results
| | | | | | ( )| | ( ) ( ) Where represents integrand that is integrated over the interval From the hypotheses it follows
| | ( )( )And analogous inequalities for . Taking into account the hypothesis the result followsRemark 1: The fact that we supposed depending also on can be considered as notconformal with the reality, however we have put this hypothesis ,in order that we can postulate condition
necessary to prove the uniqueness of the solution bounded by respectively ofIf instead of proving the existence of the solution on
, we have to prove it only on a compact then it
suffices to consider that depend only on and respectively on
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and hypothesis can replaced by a usual Lipschitz condition.Remark 2: There does not exist any where From 69 to 32 it results
{(())} () for Definition of ( )( ) ( ) :Remark 3: if is bounded, the same property have also . indeed if it follows ( ) and by integrating ( ) ( ) In the same way , one can obtain ( ) ( ) If is bounded, the same property follows for and respectively.
Remark 4: If bounded, from below, the same property holds for The proof isanalogous with the preceding one. An analogous property is true if is bounded from below.Remark 5: If
is bounded from below and
then
Definition of :Indeed let be so that for
( ) Then
which leads to
If we take
such that
it results
By taking now sufficiently small one sees that is unbounded.The same property holds for if ( ) We now state a more precise theorem about the behaviors at infinity of the solutions
Behavior of the solutions
If we denote and define
Definition of :
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(a) four constants satisfying
Definition of :(b) By and respectively the roots of the equations() and () Definition of :By and respectively the roots of the equations() and ()
Definition of
:-
(c) If we define by and
and analogously
and where are defined respectively
Then the solution satisfies the inequalities
() where is defined
() () () ( )
()
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()( )
() () Definition of :-
Where Behavior of the solutions
If we denote and define
Definition of :(d) four constants satisfying
( )
( )
Definition of :By and respectively the roots(e) of the equations ()
and () andDefinition of :By and respectively theroots of the equations () and () Definition of :-(f) If we define by and
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and analogously
and Then the solution satisfies the inequalities
()
is defined ()
() () ( ) ()
()( ) () ()
Definition of :-Where
Behavior of the solutions
If we denote and define
Definition of :(a) four constants satisfying
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( ) Definition of :(b) By
and respectively
the roots of the equations
() and () andBy and respectively theroots of the equations ()
and () Definition of :-(c) If we define by
and
and analogously
and Then the solution satisfies the inequalities
() is defined () () () ( )
() ()
( )
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() () Definition of :-
Where
Behavior of the solutions
If we denote and define
Definition of :(d) four constants satisfying ( ) ( ) Definition of :(e) By
and respectively
the roots of the equations
() and () andDefinition of :
By and respectively theroots of the equations ()
and () Definition of :-(f) If we define
by and
and analogously
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and
where
are defined by 59 and 64 respectively
Then the solution satisfies the inequalities
() where is defined
()
() () ( ) ()
()( )
() ()
Definition of :-Where
Behavior of the solutions
If we denote and define
Definition of :(g) four constants satisfying ( ) ( ) Definition of :(h) By and respectively the roots of the equations()
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and () andDefinition of :
By
and respectively
the
roots of the equations () and () Definition of :-(i) If we define by
and
and analogously
and
where
are defined respectively
Then the solution satisfies the inequalities
() where is defined () () () ( )
() ()
( ) () ()
Definition of :-Where
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Behavior of the solutionsIf we denote and define
Definition of :(j) four constants satisfying
( )
( )
Definition of :(k) By and respectively the roots of the equations()
and () andDefinition of :
By and respectively theroots of the equations
(
)
and () Definition of :-(l) If we define by
and
and analogously
and where
are defined respectively
Then the solution satisfies the inequalities
()
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where is defined () () () ( ) ()
()( )
() () Definition of :-
Where
Proof : From GLOBAL EQUATIONS we obtain
Definition of :-
It follows
() () From which one obtains
Definition of :-(a) For
,
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In the same manner , we get
, From which we deduce
(b) If we find like in the previous case,
(c) If , we obtain
And so with the notation of the first part of condition (c) , we have
Definition of :- ,
In a completely analogous way, we obtain
Definition of :- , Now, using this result and replacing it in GLOBAL EQUATIONS we get easily the result stated in the
theorem.
Particular case :
If and in this case if in addition then and as a consequence this also defines for thespecial case
Analogously if and then if in addition then This is an importantconsequence of the relation between and and definition ofwe obtain
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Definition of :- It follows
() () From which one obtains
Definition of :-(d) For
,
In the same manner , we get
, From which we deduce
(e) If
we find like in the previous case,
(f) If , we obtain
And so with the notation of the first part of condition (c) , we have
Definition of :- , In a completely analogous way, we obtain
Definition of :-
,
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.
Particular case :
If
and in this case
if in addition
then and as a consequence Analogously if and then if in addition then This is an importantconsequence of the relation between and From GLOBAL EQUATIONS we obtain
Definition of :- It follows
() () From which one obtains
(a) For , In the same manner , we get
, Definition of
:-
From which we deduce (b) If we find like in the previous case,
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(c) If , we obtain And so with the notation of the first part of condition (c) , we have
Definition of :- , In a completely analogous way, we obtain
Definition of :-
,
Now, using this result and replacing it in GLOBAL EQUATIONS we get easily the result stated in the
theorem.
Particular case :
If and in this case if in addition then and as a consequence Analogously if and then if in addition then This is an importantconsequence of the relation between
and
: From GLOBAL EQUATIONS we obtain
Definition of :-
It follows
() () From which one obtainsDefinition of :-
(d) For ,
In the same manner , we get
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, From which we deduce
(e) If we find like in the previous case,
(f) If , we obtain
And so with the notation of the first part of condition (c) , we have
Definition of :- , In a completely analogous way, we obtain
Definition of :- , Now, using this result and replacing it in GLOBAL EQUATIONS we get easily the result stated in thetheorem.
Particular case :
If and in this case if in addition then and as a consequence this also defines forthe special case .
Analogously if
and then
if in addition then This is an importantconsequence of the relation between and and definition ofFrom GLOBAL EQUATIONS we obtain
Definition of :-
It follows
() ()
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From which one obtains
Definition of :-(g) For
, In the same manner , we get
,
From which we deduce (h) If we find like in the previous case,
(i) If , we obtain And so with the notation of the first part of condition (c) , we have
Definition of :- , In a completely analogous way, we obtain
Definition of
:-
, Now, using this result and replacing it in GLOBAL EQUATIONS we get easily the result stated in the
theorem.
Particular case :
If and in this case if in addition then and as a consequence this also defines forthe special case .
Analogously if and then if in addition then This is an important
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consequence of the relation between and and definition ofwe obtain
Definition of :-
It follows() () From which one obtains
Definition of :-(j) For
, In the same manner , we get
, From which we deduce
(k) If we find like in the previous case,
(l) If , we obtain
And so with the notation of the first part of condition (c) , we have
Definition of :-
,
In a completely analogous way, we obtain
Definition of :-
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, Now, using this result and replacing it in GLOBAL EQUATIONS we get easily the result stated in the
theorem.
Particular case :
If and in this case if in addition then and as a consequence this also defines forthe special case .
Analogously if and then if in addition then This is an importantconsequence of the relation between and and definition ofWe can prove the following
Theorem 3: If are independent on , and the conditions ,
as defined, then the system
If are independent on , and the conditions ,
as defined are satisfied , then the systemIf are independent on , and the conditions , as defined are satisfied , then the systemIf
are independent on
, and the conditions
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,
as defined are satisfied , then the systemIf are independent on , and the conditions
,
as defined satisfied , then the systemIf are independent on , and the conditions
,
as defined are satisfied , then the system [ ] [ ] [ ]
has a unique positive solution , which is an equilibrium solution for the system
[ ] [ ] [ ]
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has a unique positive solution , which is an equilibrium solution for
[ ] [ ] [ ]
has a unique positive solution , which is an equilibrium solution
[ ] [ ] [ ] ()
()
() has a unique positive solution , which is an equilibrium solution for the system
[ ] [ ] [ ] has a unique positive solution , which is an equilibrium solution for the system
[
]
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[ ] [ ]
has a unique positive solution , which is an equilibrium solution for the system
(a) Indeed the first two equations have a nontrivial solution if (a) Indeed the first two equations have a nontrivial solution if
(a) Indeed the first two equations have a nontrivial solution if (a) Indeed the first two equations have a nontrivial solution if (a) Indeed the first two equations have a nontrivial solution if (a) Indeed the first two equations have a nontrivial solution
if
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Definition and uniqueness of :-After hypothesis
and the functions
being increasing, it follows that there
exists a unique for which . With this value , we obtain from the three first equations [ ( )] , [ ( )]Definition and uniqueness of :-After hypothesis and the functions being increasing, it follows that thereexists a unique for which . With this value , we obtain from the three first equations [ ( )] , [ ( )]Definition and uniqueness of :-After hypothesis and the functions being increasing, it follows that thereexists a unique for which . With this value , we obtain from the three first equations [ ( )] , [ ( )]Definition and uniqueness of :-After hypothesis and the functions being increasing, it follows that thereexists a unique
for which
. With this value , we obtain from the three first equations
[ ( )] , [ ( )]Definition and uniqueness of :-After hypothesis and the functions being increasing, it follows that thereexists a unique for which . With this value , we obtain from the three first equations [ ( )] , [ ( )]Definition and uniqueness of
:-
After hypothesis and the functions being increasing, it follows that thereexists a unique for which . With this value , we obtain from the three first equations [ ( )] , [ ( )](e) By the same argument, the equations 92,93 admit solutions if [ ] Where in must be replaced by their values from 96. It is easy to see that is adecreasing function in taking into account the hypothesis it follows that there
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exists a unique such that (f) By the same argument, the equations 92,93 admit solutions if
[ ] Where in must be replaced by their values from 96. It is easy to see that is adecreasing function in taking into account the hypothesis it follows that thereexists a unique such that (g) By the same argument, the concatenated equations admit solutions if
[
]
Where in must be replaced by their values from 96. It is easy to see that is adecreasing function in taking into account the hypothesis it follows that thereexists a unique such that (h) By the same argument, the equations of modules admit solutions if [ ] Where in
must be replaced by their values from 96. It is easy to see that
is a
decreasing function in taking into account the hypothesis it follows that thereexists a unique such that (i) By the same argument, the equations (modules) admit solutions if [ ] Where in must be replaced by their values from 96. It is easy to see that is adecreasing function in
taking into account the hypothesis
it follows that there
exists a unique such that (j) By the same argument, the equations (modules) admit solutions if [ ] Where in must be replaced by their values It is easy to see that is adecreasing function in taking into account the hypothesis it follows that thereexists a unique
such that
Finally we obtain the unique solution of 89 to 94
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, and [ ( )] , [ ( )] [ ] , [ ]Obviously, these values represent an equilibrium solution
Finally we obtain the unique solution
, and [ ( )] , [ ( )]
[ ],
[ ]
Obviously, these values represent an equilibrium solution
Finally we obtain the unique solution
, and [ ( )] , [ ( )] [ ] , [ ]Obviously, these values represent an equilibrium solution
Finally we obtain the unique solution
, and [ ( )] , [ ( )] [ ] , [ ]Obviously, these values represent an equilibrium solution
Finally we obtain the unique solution
, and [ ( )] , [ ( )] [ ] , [ ]Obviously, these values represent an equilibrium solution
Finally we obtain the unique solution
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, and [ ( )] , [ ( )] [ ] , [ ]Obviously, these values represent an equilibrium solution
ASYMPTOTIC STABILITY ANALYSIS
Theorem 4: If the conditions of the previous theorem are satisfied and if the functions Belong to then the above equilibrium point is asymptotically stable.Proof: Denote
Definition of
:-
, , Then taking into account equations (global) and neglecting the terms of power 2, we obtain
( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( ) If the conditions of the previous theorem are satisfied and if the functions Belong to then the above equilibrium point is asymptotically stableDenote
Definition of :- , , taking into account equations (global)and neglecting the terms of power 2, we obtain
( ) ( )
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( ) ( ) ( ) ( ) ( ) ( ) ( ) If the conditions of the previous theorem are satisfied and if the functions Belong to then the above equilibrium point is asymptotically stablDenote
Definition of :- , ,
Then taking into account equations (global) and neglecting the terms of power 2, we obtain
( ) ( )
(
)
( ) ( ) ( ) ( ) ( ) ( ) If the conditions of the previous theorem are satisfied and if the functions Belong to then the above equilibrium point is asymptotically stablDenote
Definition of :- , ,
Then taking into account equations (global) and neglecting the terms of power 2, we obtain
( ) ( )
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( ) ( ) ( ) ( ) ( ) ( ) ( ) If the conditions of the previous theorem are satisfied and if the functions Belong to then the above equilibrium point is asymptotically stable
Denote
Definition of
:-
, , Then taking into account equations (global) and neglecting the terms of power 2, we obtain
( )
(
)
( ) ( ) ( ) ( ) ( ) ( ) ( ) If the conditions of the previous theorem are satisfied and if the functions Belong to
then the above equilibrium point is asymptotically stable
Denote
Definition of :- , ,
Then taking into account equations(global) and neglecting the terms of power 2, we obtain
( )
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( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) The characteristic equation of this system is
(
)(
)
( ) ( ) ( ) ( ) () ( ) () ( ) () ( ) ( ) ( )
( ) +
( )( )
( ) ( ) ( ) ( )
() ( )
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() ( ) () ( ) ( ) ( )( ) +( )( )( ) ( ) ( ) ( )
() ( ) () ( ) () ( ) ( ) ( )( ) +( )( )( ) ( ) ( )
( ) () ( )
() ( )
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() ( ) ( ) ( )
( ) +
( )( )( ) ( ) ( ) ( ) () ( )
() ( ) () ( ) ( ) ( )( ) +
( )( )
(
)
( ) ( ) ( )
() ( )
(
)
(
)
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() ( ) ( ) ( )
( ) And as one sees, all the coefficients are positive. It follows that all the roots have negative real part, and this
proves the theorem.
Acknowledgments:
The introduction is a collection of information from various articles, Books, News Paper reports,
Home Pages Of authors, Journal Reviews, Nature s L:etters,Article Abstracts, Research papers,
Abstracts Of Research Papers, Stanford Encyclopedia, Web Pages, Ask a Physicist Column,
Deliberations with Professors, the internet including Wikipedia. We acknowledge all authors who
have contributed to the same. In the eventuality of the fact that there has been any act of omission on
the part of the authors, we regret with great deal of compunction, contrition, regret, trepidiation and
remorse. As Newton said, it is only because erudite and eminent people allowed one to piggy ride on
their backs; probably an attempt has been made to look slightly further. Once again, it is stated that
the references are only illustrative and not comprehensive
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Edition".
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Vol 37 (1982),Commemoration volume dedicated to Professor Akitsugu Kawaguchi on his 80th
birthday4. FRTJOF CAPRA: The web of life Flamingo, Harper Collins See "Dissipative structures pages 172-
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Encyclopedia of Life Support Systems ((EOLSS), (Eolss Publishers, Oxford) [http://www.eolss.net
6. MATSUI, T, H. Masunaga, S. M. Kreidenweis, R. A. Pielke Sr., W.-K. Tao, M. Chin, and Y. JKaufman (2006), Satellite-based assessment of marine low cloud variability associated with
aerosol, atmospheric stability, and the diurnal cycle, J. Geophys. Res., 111, D17204,
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7. STEVENS, B, G. Feingold, W.R. Cotton and R.L. Walko, Elements of the microphysical structure of
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numerically simulated nonprecipitating stratocumulus J. Atmos. Sci., 53, 980-1006
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(9)^ abcEinstein, A. (1905), "Ist die Trgheit eines Krpers von seinem Energieinhalt abhngig?",Annalen
der Physik18: 639 Bibcode 1905AnP...323..639E,DOI:10.1002/andp.19053231314. See also the English
translation.
(10)^ abPaul Allen Tipler, Ralph A. Llewellyn (2003-01),Modern Physics, W. H. Freeman and Company,
pp. 8788, ISBN 0-7167-4345-0
(11)^ab Rainville, S. et al. World Year of Physics: A direct test of E=mc2.Nature 438, 1096-1097 (22
December 2005) | doi: 10.1038/4381096a; Published online 21 December 2005.
(12)^ In F. Fernflores. The Equivalence of Mass and Energy. Stanford Encyclopedia of Philosophy
(13)^ Note that the relativistic mass, in contrast to the rest mass m0, is not a relativistic invariant, and that
the velocity is not a Minkowski four-vector, in contrast to the quantity , where is the differential of
the proper time. However, the energy-momentum four-vector is a genuine Minkowski four-vector, and the
intrinsic origin of the square-root in the definition of the relativistic mass is the distinction
between danddt.
(14)^Relativity DeMystified, D. McMahon, Mc Graw Hill (USA), 2006, ISBN 0-07-145545-0
(15)^Dynamics and Relativity, J.R. Forshaw, A.G. Smith, Wiley, 2009, ISBN 978-0-470-01460-8
(16)^Hans, H. S.; Puri, S. P. (2003).Mechanics (2 ed.). Tata McGraw-Hill. p. 433. ISBN 0-07-047360-
9., Chapter 12 page 433
(17)^E. F. Taylor and J. A. Wheeler, Spacetime Physics, W.H. Freeman and Co., NY. 1992.ISBN 0-7167-
2327-1, see pp. 248-9 for discussion of mass remaining constant after detonation of nuclear bombs, until heat
is allowed to escape.
(18)^Mould, Richard A. (2002).Basic relativity (2 ed.). Springer. p. 126. ISBN 0-387-95210-1., Chapter 5
page 126
(19)^Chow, Tail L. (2006).Introduction to electromagnetic theory: a modern perspective. Jones & Bartlett
Learning. p. 392. ISBN 0-7637-3827-1., Chapter 10 page 392
(20)^ [2] Cockcroft-Walton experiment
(21)^a
b
c
Conversions used: 1956 International (Steam) Table (IT) values where one calorie 4.1868 J and
one BTU 1055.05585262 J. Weapons designers' conversion value of one gram TNT 1000 calories used.
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1. .(22)^Assuming the dam is generating at its peak capacity of 6,809 MW.
(23)^Assuming a 90/10 alloy of Pt/Ir by weight, a Cp of 25.9 for Pt and 25.1 for Ir, a Pt-dominated
average Cp of 25.8, 5.134 moles of metal, and 132 J.K-1 for the prototype. A variation of 1.5 picograms is of
course, much smaller than the actual uncertainty in the mass of the international prototype, which are
2 micrograms.
(24)^[3]Article on Earth rotation energy. Divided by c^2.
(25)^abEarth's gravitational self-energy is 4.6 10-10 that of Earth's total mass, or 2.7 trillion metric tons.
Citation: The Apache Point Observatory Lunar Laser-Ranging Operation (APOLLO) , T. W. Murphy, Jr. et
al. University of Washington, Dept. of Physics (132 kB PDF, here.).
(26)^There is usually more than one possible way to define a field energy, because any field can be made to
couple to gravity in many different ways. By general scaling arguments, the correct answer at everyday
distances, which are long compared to the quantum gravity scale, should be minimal coupling, which means
that no powers of the curvature tensor appear. Any non-minimal couplings, along with other higher order
terms, are presumably only determined by a theory of quantum gravity, and within string theory, they only
start to contribute to experiments at the string scale.
(27)^G. 't Hooft, "Computation of the quantum effects due to a four-dimensional pseudoparticle", Physical
Review D14:34323450 (1976).
(28)^A. Belavin, A. M. Polyakov, A. Schwarz, Yu. Tyupkin, "Pseudoparticle Solutions to Yang Mills
Equations", Physics Letters 59B:85 (1975).
(29)^F. Klinkhammer, N. Manton, "A Saddle Point Solution in the Weinberg Salam Theory", Physical
Review D 30:2212.
(30)^Rubakov V. A. "Monopole Catalysis of Proton Decay", Reports on Progress in Physics 51:189241
(1988).
(31)^S.W. Hawking "Black Holes Explosions?"Nature 248:30 (1974).
(32)^Einstein, A. (1905), "Zur Elektrodynamik bewegter Krper." (PDF),Annalen der Physik17: 891
921, Bibcode 1905AnP...322..891E,DOI:10.1002/andp.19053221004. English translation.
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(33)^See e.g. Lev B.Okun, The concept of Mass, Physics Today 42 (6), June 1969, p. 31
36, http://www.physicstoday.org/vol-42/iss-6/vol42no6p31_36.pdf
(34)^Max Jammer (1999), Concepts of mass in contemporary physics and philosophy, Princeton University
Press, p. 51, ISBN 0-691-01017-X
(35)^Eriksen, Erik; Vyenli, Kjell (1976), "The classical and relativistic concepts of mass",Foundations of
Physics (Springer) 6: 115124, Bibcode 1976FoPh....6..115E,DOI:10.1007/BF00708670
(36)^ abJannsen, M., Mecklenburg, M. (2007), From classical to relativistic mechanics: Electromagnetic
models of the electron., in V. F. Hendricks, et al., ,Interactions: Mathematics, Physics and
Philosophy (Dordrecht: Springer): 65134
(37)^abWhittaker, E.T. (19511953), 2. Edition: A History of the theories of aether and electricity, vol. 1:
The classical theories / vol. 2: The modern theories 19001926, London: Nelson
(38)^Miller, Arthur I. (1981),Albert Einstein's special theory of relativity. Emergence (1905) and early
interpretation (19051911), Reading: AddisonWesley, ISBN 0-201-04679-2
(39)^abDarrigol, O. (2005), "The Genesis of the theory of relativity." (PDF), Sminaire Poincar1: 122
(40)^Philip Ball (Aug 23, 2011). "Did Einstein discover E = mc2?". Physics World.
(41)^Ives, Herbert E. (1952), "Derivation of the mass-energy relation",Journal of the Optical Society of
America42 (8): 540543, DOI:10.1364/JOSA.42.000540
(42)^ Jammer, Max (1961/1997). Concepts of Mass in Classical and Modern Physics. New York:
Dover. ISBN 0-486-29998-8.
(43)^Stachel, John; Torretti, Roberto (1982), "Einstein's first derivation of mass-energyequivalence",American Journal of Physics50 (8): 760
763, Bibcode1982AmJPh..50..760S, DOI:10.1119/1.12764
(44)^Ohanian, Hans (2008), "Did Einstein prove E=mc2?", Studies In History and Philosophy of Science
Part B40 (2): 167173, arXiv:0805.1400,DOI:10.1016/j.shpsb.2009.03.002
(45)^Hecht, Eugene (2011), "How Einstein confirmed E0=mc2",American Journal of Physics79 (6): 591
600, Bibcode 2011AmJPh..79..591H, DOI:10.1119/1.3549223
(46)^Rohrlich, Fritz (1990), "An elementary derivation of E=mc2",American Journal of Physics58 (4):
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