Natures General Ledger

7/31/2019 Natures General Ledger

1/74

Information and Knowledge Management www.iiste.orgISSN 2224-5758 (Paper) ISSN 2224-896X (Online)

Vol 2, No.4, 2012

45

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)


2/74


Vol 2, No.4, 2012

46

(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


3/74


Vol 2, No.4, 2012

47

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


4/74


Vol 2, No.4, 2012

48

: 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

,


5/74


Vol 2, No.4, 2012

49

are Dissipation coefficientsThe differential system of this model is now (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

[ ] [ ] [ ]


6/74


Vol 2, No.4, 2012

50

[ ] [ ] [ ] First augmentation factor First detritions factor

MASS AND ENERGY:MODULE NUMBERED FOUR:

The differential system of this model is now (Module numbered Four)

[ ] [ ] [ ] [ ()] [ ()] [ ()]


( ) First detritions factorThe differential system of this model is now (Module number five)

VACUUM ENERGY AND QUANTUM FIELD:MODULE NUMBERED FIVE

[ ] [ ]

[ ] [ ()] [ ()] [ ()]



7/74


Vol 2, No.4, 2012

51

( ) 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


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


8/74


Vol 2, No.4, 2012

52

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


9/74


Vol 2, No.4, 2012

53

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


10/74


Vol 2, No.4, 2012

54

, 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


11/74


Vol 2, No.4, 2012

55

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

, , ,


12/74


Vol 2, No.4, 2012

56

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


13/74


Vol 2, No.4, 2012

57

- 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


14/74


Vol 2, No.4, 2012

58

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:

( )


15/74


Vol 2, No.4, 2012

59

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


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 :


16/74


Vol 2, No.4, 2012

60

(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


( )

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


17/74


Vol 2, No.4, 2012

61

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


18/74


Vol 2, No.4, 2012

62

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


19/74


Vol 2, No.4, 2012

63

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


20/74


Vol 2, No.4, 2012

64

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


21/74


Vol 2, No.4, 2012

65

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


22/74


Vol 2, No.4, 2012

66

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


23/74


Vol 2, No.4, 2012

67

(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 ( )



24/74


Vol 2, No.4, 2012

68

( )

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 ( )


(

)

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

( )


( )

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 ( )

(

)


25/74


Vol 2, No.4, 2012

69

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


26/74


Vol 2, No.4, 2012

70

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 ( ) ( )

|

|

|

|


27/74


Vol 2, No.4, 2012

71

Indeed if we denote

Definition of : ( ) It results





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


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.


28/74


Vol 2, No.4, 2012

72

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

| | | | | | ( )| | ( ) ( )


29/74


Vol 2, No.4, 2012

73

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


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.


30/74


Vol 2, No.4, 2012

74

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


31/74


Vol 2, No.4, 2012

75



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


32/74


Vol 2, No.4, 2012

76

It is now sufficient to take and to choose

large to have

( )

( )


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


33/74


Vol 2, No.4, 2012

77

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


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


34/74


Vol 2, No.4, 2012

78

It is now sufficient to take and to choose

large to have ( ) ( )


Definition of : ( ) ( )It results





suffices to consider that depend only on and respectively on


35/74


Vol 2, No.4, 2012

79

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 :


36/74


Vol 2, No.4, 2012

80

(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

() () () ( )

()


37/74


Vol 2, No.4, 2012

81

()( )

() () Definition of :-

Where Behavior of the solutions


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


38/74


Vol 2, No.4, 2012

82

and analogously

and Then the solution satisfies the inequalities

()

is defined ()

() () ( ) ()

()( ) () ()

Definition of :-Where



Definition of :(a) four constants satisfying


39/74


Vol 2, No.4, 2012

83

( ) 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 () () () ( )

() ()

( )


40/74


Vol 2, No.4, 2012

84


Where



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


41/74


Vol 2, No.4, 2012

85

and

where

are defined by 59 and 64 respectively


() where is defined

()

() () ( ) ()

()( )

() ()




Definition of :(g) four constants satisfying ( ) ( ) Definition of :(h) By and respectively the roots of the equations()


42/74


Vol 2, No.4, 2012

86

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


() where is defined () () () ( )

() ()

( ) () ()



43/74


Vol 2, No.4, 2012

87

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


()


44/74


Vol 2, No.4, 2012

88

where is defined () () () ( ) ()

()( )


Where

Proof : From GLOBAL EQUATIONS we obtain

Definition of :-

It follows

() () From which one obtains

Definition of :-(a) For

,


45/74


Vol 2, No.4, 2012

89

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


46/74


Vol 2, No.4, 2012

90

Definition of :- It follows


Definition of :-(d) For

,



(e) If

we find like in the previous case,

(f) If , we obtain


Definition of :- , In a completely analogous way, we obtain

Definition of :-

,


47/74


Vol 2, No.4, 2012

91

.

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


(a) For , In the same manner , we get

, Definition of

:-

From which we deduce (b) If we find like in the previous case,


48/74


Vol 2, No.4, 2012

92

(c) If , we obtain And so with the notation of the first part of condition (c) , we have


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 ,



49/74


Vol 2, No.4, 2012

93


(e) If we find like in the previous case,

(f) If , 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

() ()


50/74


Vol 2, No.4, 2012

94

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

:-

, Now, using this result and replacing it in GLOBAL EQUATIONS we get easily the result stated in the

theorem.

Particular case :


Analogously if and then if in addition then This is an important


51/74


Vol 2, No.4, 2012

95

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


(k) If we find like in the previous case,

(l) If , we obtain


Definition of :-

,

In a completely analogous way, we obtain

Definition of :-


52/74


Vol 2, No.4, 2012

96

, Now, using this result and replacing it in GLOBAL EQUATIONS we get easily the result stated in the

theorem.

Particular 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


53/74


Vol 2, No.4, 2012

97

,

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

[ ] [ ] [ ]


54/74


Vol 2, No.4, 2012

98

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

[

]


55/74


Vol 2, No.4, 2012

99

[ ] [ ]

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


56/74


Vol 2, No.4, 2012

100

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


57/74


Vol 2, No.4, 2012

101

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


58/74


Vol 2, No.4, 2012

102

, and [ ( )] , [ ( )] [ ] , [ ]Obviously, these values represent an equilibrium solution

Finally we obtain the unique solution

, and [ ( )] , [ ( )]

[ ],

[ ]

Obviously, these values represent an equilibrium solution









59/74


Vol 2, No.4, 2012

103


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

( ) ( )


60/74


Vol 2, No.4, 2012

104

( ) ( ) ( ) ( ) ( ) ( ) ( ) 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


Then taking into account equations (global) and neglecting the terms of power 2, we obtain

( ) ( )


61/74


Vol 2, No.4, 2012

105

( ) ( ) ( ) ( ) ( ) ( ) ( ) 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


Then taking into account equations(global) and neglecting the terms of power 2, we obtain

( )


62/74


Vol 2, No.4, 2012

106

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) The characteristic equation of this system is

(

)(

)

( ) ( ) ( ) ( ) () ( ) () ( ) () ( ) ( ) ( )

( ) +

( )( )

( ) ( ) ( ) ( )

() ( )


63/74


Vol 2, No.4, 2012

107

() ( ) () ( ) ( ) ( )( ) +( )( )( ) ( ) ( ) ( )

() ( ) () ( ) () ( ) ( ) ( )( ) +( )( )( ) ( ) ( )

( ) () ( )

() ( )


64/74


Vol 2, No.4, 2012

108

() ( ) ( ) ( )

( ) +

( )( )( ) ( ) ( ) ( ) () ( )

() ( ) () ( ) ( ) ( )( ) +

( )( )

(

)

( ) ( ) ( )

() ( )

(

)

(

)


65/74


Vol 2, No.4, 2012

109

() ( ) ( ) ( )

( ) 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

REFERENCES

1. Dr K N Prasanna Kumar, Prof B S Kiranagi, Prof C S Bagewadi -MEASUREMENT DISTURBSEXPLANATION OF QUANTUM MECHANICAL STATES-A HIDDEN VARIABLE THEORY -

published at: "International Journal of Scientific and Research Publications, Volume 2, Issue 5, May 2012

Edition".

2. DR K N PRASANNA KUMAR, PROF B S KIRANAGI and PROF C S BAGEWADI -CLASSIC 2FLAVOUR COLOR SUPERCONDUCTIVITY AND ORDINARY NUCLEAR MATTER-A NEW

PARADIGM STATEMENT - published at: "International Journal of Scientific and Research Publications,

Volume 2, Issue 5, May 2012 Edition".3. A HAIMOVICI: On the growth of a two species ecological system divided on age groups. Tensor,

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-

188

5. HEYLIGHEN F. (2001): "The Science of Self-organization and Adaptivity", in L. D. Kiel, (ed) .Knowledge Management, Organizational Intelligence and Learning, and Complexity, in: The

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,

doi:10.1029/2005JD006097

7. STEVENS, B, G. Feingold, W.R. Cotton and R.L. Walko, Elements of the microphysical structure of
http://www.ijsrp.org/research_paper_may2012/rp34.htmlhttp://www.ijsrp.org/research_paper_may2012/rp34.htmlhttp://www.ijsrp.org/research_paper_may2012/rp34.htmlhttp://www.ijsrp.org/research_paper_may2012/rp34.htmlhttp://www.ijsrp.org/research_paper_may2012/rp35.htmlhttp://www.ijsrp.org/research_paper_may2012/rp35.htmlhttp://www.ijsrp.org/research_paper_may2012/rp35.htmlhttp://www.ijsrp.org/research_paper_may2012/rp35.htmlhttp://www.ijsrp.org/research_paper_may2012/rp35.htmlhttp://pcp.lanl.gov/papers/EOLSS-Self-Organiz.pdfhttp://pcp.lanl.gov/papers/EOLSS-Self-Organiz.pdfhttp://www.ijsrp.org/research_paper_may2012/rp35.htmlhttp://www.ijsrp.org/research_paper_may2012/rp35.htmlhttp://www.ijsrp.org/research_paper_may2012/rp35.htmlhttp://www.ijsrp.org/research_paper_may2012/rp34.htmlhttp://www.ijsrp.org/research_paper_may2012/rp34.html


66/74


Vol 2, No.4, 2012

110

numerically simulated nonprecipitating stratocumulus J. Atmos. Sci., 53, 980-1006

8. FEINGOLD, G, Koren, I; Wang, HL; Xue, HW; Brewer, WA (2010), Precipitation-generatedoscillations in open cellular cloud fields Nature, 466(7308) 849-852, doi: 10.1038/nature09314,

Published 12-Aug 2010
http://dx.doi.org/10.1038/nature09314http://dx.doi.org/10.1038/nature09314


67/74


Vol 2, No.4, 2012

111

(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)âb 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)Ê. 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)â

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.
http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-inertia_0-1http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-inertia_0-1http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-inertia_0-2http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-inertia_0-2http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-inertia_0-2http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-tipler_1-1http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-tipler_1-1http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-tipler_1-1http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-rainville_2-0http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-rainville_2-0http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-rainville_2-0http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-5http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-5http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-5http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-6http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-6http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-6http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-7http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-7http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-7http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-8http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-8http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-8http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-9http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-9http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-9http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-10http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-10http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-10http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-10http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-9http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-8http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-7http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-6http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-5http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-rainville_2-0http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-tipler_1-1http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-inertia_0-2http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-inertia_0-1


68/74


Vol 2, No.4, 2012

112

1. .(22)Âssuming the dam is generating at its peak capacity of 6,809 MW.

(23)Âssuming 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)âbEarth'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)Â. 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)Êinstein, A. (1905), "Zur Elektrodynamik bewegter Krper." (PDF),Annalen der Physik17: 891

921, Bibcode 1905AnP...322..891E,DOI:10.1002/andp.19053221004. English translation.
http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-14http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-14http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-14http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-15http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-15http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-15http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-16http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-16http://infranetlab.org/blog/2008/12/harnessing-the-energy-from-the-earth%E2%80%99s-rotation/http://infranetlab.org/blog/2008/12/harnessing-the-energy-from-the-earth%E2%80%99s-rotation/http://infranetlab.org/blog/2008/12/harnessing-the-energy-from-the-earth%E2%80%99s-rotation/http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-apollo_17-0http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-apollo_17-0http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-apollo_17-1http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-apollo_17-1http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-apollo_17-1http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-18http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-18http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-18http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-19http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-19http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-19http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-20http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-20http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-20http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-21http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-21http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-21http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-22http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-22http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-22http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-23http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-23http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-23http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-24http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-24http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-24http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-24http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-23http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-22http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-21http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-20http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-19http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-18http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-apollo_17-1http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-apollo_17-0http://infranetlab.org/blog/2008/12/harnessing-the-energy-from-the-earth%E2%80%99s-rotation/http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-16http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-15http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-14


69/74


Vol 2, No.4, 2012

113

(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)Êriksen, 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)âbWhittaker, 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)âbDarrigol, 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)Îves, 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)Ôhanian, 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):
http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-26http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-26http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-26http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-Jammer_27-0http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-Jammer_27-0http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-Jammer_27-0http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-V.C3.B8yenli_28-0http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-V.C3.B8yenli_28-0http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-V.C3.B8yenli_28-0http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-jann_29-1http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-jann_29-1http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-jann_29-1http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-whit_30-0http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-whit_30-0http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-whit_30-1http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-whit_30-1http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-whit_30-1http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-mill_31-0http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-mill_31-0http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-mill_31-0http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-darr_32-0http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-darr_32-0http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-darr_32-1http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-darr_32-1http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-darr_32-1http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-33http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-33http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-33http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-34http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-34http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-34http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-36http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-36http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-36http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-37http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-37http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-37http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-38http://en.wikipedia.org/wiki/Conservation_of_mass-energy#cite_ref-38http://en.wikipedia.org/wiki/Conservation_of_mass-energ

Natures General Ledger

Documents

Transcript of Natures General Ledger