The creation of electron
Based on the gap space theory
Shogo Niimi
shogo-ni@sk2.aitai.ne.jp
August 31th, 2004<< Contents >>[1]. Unit system of the expressions(a) Electromagnetic field and the light velocity////////P2(b) Expressions

P4[2]. Electric charge(a) Theoretical expression of the electric charge///////P6(b) Value of the electric charge////////////////////////P8(c) Fractional charge///////////////////////////////////P9(d) Fine-structure constantP11[3]. Electronic mass(a) Consider of the existent mass expression////////////P12(b) Electronic mass/////////////////////////////////////P15(c) g-factor////////////////////////////////////////////P18- １ -[1]. Unit system of the expressions(a) Electromagnetic field and the light velocity
I could not give a lot of expressions that were gotten in the <<Pair productionof light velocity c with Planck’s constant >> the unit dimension. Here, I
will reconsider them. Incidentally, the unit dimension system is [VAMS].
<<"The electromagnetic unit is not difficult" Imai Isao, January 2002, KAGAKU, Iwanami co.>>The expression of light velocity iscωj2exp(+ρj)cosδjvj=(σj2+ωj2)[m1s-1]

ρj =σjτδj =ωjτ

[1-1]

・・・・
The relation between electric field E and magnetic field B are

・・・・
and

E
1
=
B
(ε0μ0)1/2
・・・・

E [V1m-1]

ε0E2
B2
=
2
2μ0

B [A1m-1][V1A-1][m1s-1]

=c

[1-2]

[1-3]

Here,ε0 has the dielectric constant and μ0 has the magnetic permeability.
You should pay attention here that the unit dimension has in therelation
1 -1

1 -1

[1-4]

・・・・ [V A ] ≡ [m s ]from [1-3]. In the above, find that the ratio of light velocity c and Planck’s
constant  is represented as follows

-43=
3.51767×10c[V1A1m-1s3]≡[A2s2]

・・・・
It has the unit dimension of the electric charge squared.
I have any other important things. Get

- ２ -

[1-5]

CaseＡ

Conditionwjτ= 48.87668
θj =4.21671×10-7-14

Solution QR = 3.21814×10・・δj = 0.00001312066853 π
2
QI = 1.7487×10-13

set same condition with Case④ on the <<Pair production of light velocity cwith Planck’s constant >> in the complex function

Qωj2exp(-iρj)cosδjQj=(σj2+ωj2)

[1-6]

・・・・
that is find from [1-1].
QR is a solution in the real space and QI is in theimaginary space (CaseA).
Absolute value |Qj| of Qj is
-13

・・・・

[1-7]

|Q j| = 1.77807×10

Here, I consider product c by .
-26

1 1 1 1・・・・ c= 3.16153×10

2 2[V A m s ]≡[V s ][1-8]

has the unit dimension of the magnetic charge (the magnetic flux) squared.
The square root of c is
1/2

・・・・ (c)

-13

1 1

= 1.77807×10[V s ][1-9]

You pay attention to [1-7] and [1-9] are the same value. Now, Qj may
have the unit dimension of the magnetic charge. If accept here, I can give
all expressions the unit dimension. I will collect expressions that are true.
This is valuable work for us.

- ３ -(b) Expressions
I gave many expressions of the <<Pair production of light velocity c with
Planck’s constant >> the symbol in expedient. Here, correct them to thegeneral symbol on the physical, as follows.
・・・・/

f (θj ) = ±R ωj exp(±ρj ) cosδj[1-10][m1s-2]

Acceleration[V1A-1s-1]

Cj ; Capacity

M j = ωj exp(-ρj )cosδj[A2m1]

Moment of force

Ёj = |M j |[V1A1s1]

Energy[V1]Electric potential

aj = cωj exp(+ρj )cosδj
1/Cj = | aj |V-j = Vωj exp(-iρj )cosδj・ ・・・

Elementary-function

V+j = Vωj exp(+iρj )cosδj[1-11]cωj2exp(+ρj )cosδjvj =(σj2+ωj2)[m1s-1](Light)VelocityΩj = |vj |[V1A-1]

Resistanceωj2exp(-ρj )cosδjj =(σj2+ωj2)

1 1 2

Angular momentum[V A s ]Planck's constant[A2m1s1]|j |Qωj2exp(-iρj )cosδj
Q-j =(σj2+ωj2)
Qωj2exp(+iρj )cosδjQ+j =(σj2-ωj2)
・・・/・

- ４ -

Magnetic chage(flux)[V1s1] = [A1m1](Magnetic radius ratio)[1-12]

cωj3exp(+ρj )cosδjrj =(σj2+ωj2)2[m1]

LengthLj = |rj |[V1A-1s1]

Inductanceωj3exp(-ρj )cosδj
Ij =(σj2+ωj2)2[V1A1s3]

Moment of inertia[A2m1s2]|Ij |Uωj3exp(-iρj )cosδj
U-j =(σj2+ωj2)2
Uωj3exp(+iρj )cosδjU+j =(σj2-ωj2)2・・・・/Electric moment[V1s2] = [A1m1s1][1-13]I am careful in the existence of singularity ( in case of θj =π/4 ) in Q+j
and U+j.
Also, the < magnetic radius ratio > means ratio with magnetic moment
μe and radius of electron re. I explain this detail to you later.
Moreover, I can get the high-order integration. I write them down
according to need.

- ５ -[2]. Electric charge(a) Theoretical expression of the electronic charge
Now, I got that find the expression of the electric charge theoretically.
However, there are the many forms. (/c)1/2 is one of form that already I
got it in chapter [1]. But, my goal is to get the experiment value of theelectric charge. Here, I will make it・・・・

e = 1.60217×10-19[A1s1][2-1]

The expression of electric charge qj is represented as・・・・

qj = Aj tj[2-2]

in electric current Aj and time tj.
I make electric current Aj

Aj =

Mj

M j ; Moment of force

[A1]

Q-j

・・・・
By the way, Aj is useless in this form.

Q-j ; Magnetic charge[2-3]

Because I understand what “wj” thathas the infinity mathematically and does not determine physically comes out
on Mj. The detail of this expression is

M j = ωj exp(-ρj ) cosδj
[2-4]
・・・・

= wj sinθj exp(-wjτcosθj ) cos (wjτsinθjρj = σjτδj = ωjτ= w τcosθjj・・・・・・・
However, the expression that I need is qj.
Aj by tj. Therefore, I will make・・・・

t j = τsinθj= wjτsinθjAs [2-2], I get qj by product[2-5]

By this expression, both of wj and tj that unsettled independently and havethe time dimension are woven.

- ６ -

・・・・

48.87668≦ wjτ≦48.901915[2-6]

I had already gotten this value.
Next, I reassemble expression qj of the electric charge.

qj=
=
・・・・

Now, can get

M jτ sinθ j
Qj[e] w jτ exp (-ρ j )cosρ j - i sinρ j[e] ;Symbol of theelectric charge[2-7]

by expressions [2-2], [2-3]. Get [e] by the combination of  with Q that ismere symbol.
By the way, we already discussed that the imaginary part does not occur
in the real space, you can see [Sheet1] and [Graph2]. I consider it, theexpression of the electric charge is

qj=
・・・・
Then,

[e] wjτexp (-wjτcosθj )cos (wjτcosθj )[2-8]kτsinθk
Uk

[2-9]

qk=

・・・・
is the form of the electric charge to similar [2-8].

You must pay attention

that do not lose sight of the essence of electron, however

・・・・

qj=

wjτM jVj[2-10]

=

wjτj
Qj

[2-11]

=

wjτIj
Uj

[2-12]

are same forms.

- ７ -(b) Value of the electric charge

I need microcomputer and calculation software at least to find the value ofthe electric charge. I have results of many computations on anotherproblem.
I should do now is to find the value of “wjτ” in each condition.
For example, the value of “wjτ” depends on the each case that “ωjτ” is
π/4 or π/3. The method that we search “wjτ” for

j
vj

≡


c

[2-13]

・・・・
is formed. After that, I should substitute the value for [2-8]. In fourcases, the results are as follows ([CaseA], [CaseB], [CaseC], [CaseD]).

CaseA

ConditionA

SolutionA

CaseB

ConditionB

SolutionB

CaseC

ConditionC

SolutionC

CaseD

・・・・

ConditionD

SolutionDω1τ= 0.00001321066853π/2[rad1]

w1τ= 48.87668[rad1]

θ1 = 4.21671×10-7[rad1]

q 1 = 1.60167×10-19[A1s1]

ω2τ= Θ(0.955316618)[rad1]

w2τ= 48.886015[rad1]

θ2 = 0.01954296[rad1]

q 2 = 1.60198×10-19[A1s1]

ω3τ= 1.23788593[rad1]

w3τ= 48.892354[rad1]

θ3 = 0.02532135[rad1]

q 3 = 1.60217×10-19[A1s1]

ω4τ= 0.999999999890292π/2[rad1]

w4τ= 48.901915[rad1]

θ4 = 0.032126893[rad1]

q 4 = 1.60249×10-19[A1s1]

Also, I list their details in [Sheet2].

- ８ -(c) Fractional charge

I should catch real electric charge qj that is the scalar of vector P in
three-dimensional space [Fig.3]. Below, I replace P in [Fig.3] with q.
q is

q = ( qx , qy , qz )[2-14]| q |= q j・・・・= ( qx2 + qy2 + qz2 )1/2

[2-15]

because it is composed by three dimensional axes of x, y and z.
I can calculate only one element of [2-14]. However, this method does
not get to have resolved it into each element. Actually, I can understandthat the value of each element exists mathematically but it is impossible forme to take it out in mathematically and physically then consider about
scalar |q| in expression [2-15].
It is the reason why the fractional charge does not exist in nature.
I discuss below the purpose of the comparison between existent theory
and this theory.
The fractional charge of the quark is given in case of angle δk that has

Θ= 0.955316618 [rad]δk = Θ

k=x,y,z・・・・
between vector q and each dimension.

[2-16]The baryon has the electric chargeand each2

q k2= q cos δ k
=
・・・・

1
3

[2-17]

is distributed three quarks respectively.
electric charge qj is・・・・

q j = ( qx2 + q*x2 )1/2

In case of the expression that

[2-18]- ９ -q*x = q sinδx= ( q cosδy , q cosδz )q * x2 =・・・・

2
3

it is equivalent to the electric charge distribution as the meson that iscomposed by two quarks. In other words, one quark has 1/3 electric charge
and another one has 2/3 electric charges.
The cube is one representative that angle Θ is stable. Vector P has adiagonal line which on a vertex (0,0,0) and (1,1,1) as the scalar.
Therefore, this vector P is not possible to move when the cube sides arestable. If vector P is the same as vector q, it is guaranteed that the electriccharge is stable (The proof omission).
I can describe the “quark confinement” in the reason that is the same as
the process that the fractional electric charge does not exist in nature.
You refer to the <<Pair production of light velocity c with Planck’s
constant >>.

- １０ -

(d) Fine-structure constant

I get

β=

(/c)
q j2

= 1.37036×10-5

・・・・[dimensionless][2-19]

from [1-5]. This mean is fine-structure constant α, and get

1= 4πε0 c2β
α・・・・= 137.036[dimensionless]2[dimensionless]

if I accept
・・・・

4πε 0 c = 1×107- １１ -[2-20]

[3]. Electronic mass(a) Consider of existent mass expression

I know that a lot of pioneers got a lot of expressions include electronic mass
me. I take some expressions out from them.
①

The relation between me and the radius of electron

The expression that classical radius of electron re is as follows.
2
rq = eme= 2.81794092×10-8
re =
・・・・
②

[m1]

[3-1]

[m1]

[3-2]

rq
4πε0 c2= 2.81794092×10-15

The relation between me and the magnetic moment

Bohr magneton μb is as follows.

μb = e2me・・・・= 9.2740154×10-24[A1m2] ( = [V1m1s1] )[3-3]

Experiment value μe of the magnetic moment is as follows.

μe = g'e
2me・・・・= 9.2847701×10-24[A1m2]

Here, g' is gotten from the g-factor, as follows.

- １２ -

[3-4]

g' =
・・・・

g
2

= 1.00115965226[3-5]

The relation between me and the electric current

③

I get

me =

Aj qj
vj

[3-6]

・・・・
from [2-3]. This [3-6] is composed by velocity vj, electric current Aj andelectron qj.

By the way, I cannot get the value of me use these expressions. So, they
have a big problem. It is that I do not decide the value one set of ωτ,must decide the value of isolated ω or τ that are in these expressions.
However, I cannot find the logical limitation which decides the value ofisolated ω or τ.
The ratio of electron radius rq and Bohr magneton μb is as follows.

μb
Φe
=
rq
2
= 3.29106×10-16[V1s1][3-7][V1s1][3-8]

Φe = 
qj

・・・・= 6.58212×10-16

Φe is the physical quantity which is called the magnetic charge or themagnetic flux. Also, the < magnetic radius ratio > that was found before is
this Φ e. This one has the unit dimension which is the same as Qj.
Unfortunately, this discussion does not develop any more. However, wehave the harvest that magnetic charge Φe has the possibility to exist as thephysical substance.
Now, I replace symbol me with electronic mass to mq, so electric charge qj- １３ -

has width was gotten in chapter [2].
By the way, does some hint go out of electric current Aj?

Aj-12
c = 5.68566×10・・・・[A1m1s-1] = [V1]

Actually,[3-9]( vj = c )is gotten as the expectation value, but it is not a logical answer because thevalue of ω or τ does not decided. I state that this expectation value isgotten as the ratio of the expression to enumerate by the following to the endof this section.

？・・？

Aj
mq
=
=
c
qj

qj
rq

=


2μb

- １４ -[V1][3-10]

(b) Electronic mass

I understood that electronic mass could not be gotten from existent theory.
Will seek electronic mass while search for the answer of “why does it so”.
Now, I reconsider about all value solutions that were gotten.
I am convinced that all value in addition to light velocity c, Planck’s
constant  and electric charge qj that finds them out has contents. Also I
believe what a lot of singularities that are expressed in the place around qj
have a meaning. For example, the expression

Qωj2 exp (+iρj ) cosδjQ+j =(σj2-ωj2 )1 1[1-12][V s ]
・・・・
has a solution of smooth vibration but I know that it has a singularity to thepoint of θ=π/4. In the near future, you can make the physical meaning of
it clear.
I state that the value in this paper is all of them in the physics.
Actually, I can find electronic mass mq out under the firm conviction.
I state repeatedly that the electric charge on this theory has the width of・・・・・1.60167×10-19 ≦ qｊ≦ 1.60249×10-19・・・・・・・・・/[3-11]
・・・・・⊿q = 8.2×10-23・・・・・・・・・・・・・・・・・・・[3-12]

It has cause to two kinds that・・・・・48.87668 ≦ wｊτ≦48.901915・・・・・・・・・・・・・[3-13]
・・・・・⊿wτ = 0.025235・・・・・・・・・・・・・・・・・,//[3-14]

also
・・・・・0 ≦θｊ≦ 0.032126893・・・・・・・・・・・・・・・//[3-15]
・・・・・⊿θ = 0.032126893・・・・・・・・・・・・/,・・・・ [3-16]

in the fluctuation width of micro angle.
charge qj has width is in- １５ -The direct cause that electric・・・・・⊿ωτ = ⊿wτ・sin⊿θ・・・・・・・・・・・・・・///[3-17]
・・・・・・・,  ⊿wτ・⊿θ・・・・・・・・・・・・・・・///[3-18]

which is composed by ⊿wτ and ⊿θ. This ⊿ωτ is the curvature angle
in the space accompanies electric charge qj which I pictured in [Fig.6] or the
motion of precession angle φ. Yes, I should say that electric charge qj isborn by the effect that the motion of precession angle
・・・・・φ = ⊿ωτ・・・・・・・・・・・・・・・[Fig.11]・ [3-19]

appears by the space has the curvature.
In this way, I can not find electric mass mq out by ignore the motion ofprecession angle φ. As I considered in [3]-(a), this is the biggest reason
that cannot get electron mass me from all existent expressions.
By the way, I define ⊿q from another point before make a mass function.
It will be


n

⊿q =

Aj dτ

j=1

・？？・

= max:q - min:q[3-20]

from the relation between electric charge qj and electric current Aj.
Aj is impossible to calculation in case of [j=0] that has θ=0 (reference to[Sheet2]). So, I delete the case of j=0. Case [j=1] has condition [a  0,
θ<a, θ≠0 ]. So, I do not need to make fix
・・・・・θ = 1.77807×10-13・・・・・・・・・・・・・・・・・ [3-21]

on it. Case [j= n] is last one.
Let’s see [Fig.10]. Expression [3-18] is a base under the existencearea of electric charge qj. Then, I understand that ⊿q is fluctuation rangeof the electric charge in the micro fluctuation angle, i.e. the motion ofprecession angle φ.
Then, I bring in fine-structure constant β to here that the condition to
get electronic mass mq assembles.
Therefore, I get- １６ -

・・・・・m*ｑ = ⊿q・β・⊿wτ・⊿θ・・・・・・・・//・・・・[3-22]
・・・・・///・ = 9.1100458×10-31・・・・・・・・・・・・・・・ [3-23]

from the interesting mass function.
The mass function that I can be logically satisfied is as follows.
・・・・・mｑ = ⊿q・β・sin⊿ωτ・・・・・・・・・・・・・・//[3-24]
・・・・・・/ = 9.1084777×10-31・・・・・・・・・・・・・・・・[3-25]

Incidentally, I must make・・・・・sin⊿ωτ・ ・ ・> [V1m-2s2]

to adjust the unit dimension.
The electronic mass that was gotten from the experiment is・・・・・mｅ = 9.1093897×10-31・・・・・・・[V1A1m-2s3]・・・・・・・・mｅ mｑ m*ｑ
What is the cause of the difference of these solutions?
curvature of the space has this cause, too.

/[3-26]

I think that the

Therefore, I want to pursue the curvature of the space to confirm rightwith mass function mq that was gotten here.

- １７ -

(c) g-factor

I already describe that the image of the motion of precession has been
pictured in [Fig.11] ,  and . Let’s discuss while we look thissometimes.
Moment of force M is composed by moment of inertia I with angularacceleration α, as follows.
・・・・・Ｍ = Iα・・・・・・・・・・(Ｉ= ｍｒ2)・・・・・・・ [3-27]

Magnetic moment μ is composed as follows by magnetic field H with M.

μ=М

[3-28]

H・・・・
By the way, we discussed that the motion of precession and mass do notexist if the space does not have curvature Φ. This mean is that the “arm”
does not exist which produces M. In other words, the space does not havemeasurement of the length, as the result it connects with that the space
itself does not exist.
As you know, get the magnetic moment of electron μb from the pointthat electronic mass is known. As for this, curvature Φ in the space does
not considered. In this case, the theoretical value should
・・・・・μｂ = 0・・・・・・(∴ Φ = 0 )・・・・・・・・・・・ [3-29]

However, I dare try for the contradiction that cannot ignore theexistence of the value. Then, I can understand that α in [3-27] is・・・・・α = gʼa・・・・・・ = a・・・・・・/(∴ gʼ= 1 )・・・・・・・・・・・//[3-30]

After all, I need the operation that finds the g-factor
・・・・

g'= 1.00115965226[3-5]

to make μb coincide with μe.
How do I get the value that is equivalent to the g-factor from the gap- １８ -

space theory ?
I make vector P that has the angle is the inclination axis of electron Θ
on [Fig.11].
・・・・・ωjτ = Θ・・・・・・・ = 0.955316618・・・・・[rad]・・・・・・・・・ [3-31]

Then, I must make the inclination angle of P・・・・・

δａ = Θ+φ・・・・・

δｂ = Θ-φ・・・・・・・・・・・・・・・・・・・[3-32]

on [Fig.11] ,  that

I consider the motion of precession angle φ.

Incidentally, I get・・・・・φ = 8.1058268×10-4・・・・・・・・・・・・・・・・・[3-33]

from [3-19].
Here, I take the cosine ratio of P' in ,  to vector P in space , get theratio of  in the “opened space” and  in the “closed space”.

Opend space

g'a=

cosΘ
cos(Θ +φ)

= 1.001148
Closed space・・・・[3-34]

g'b= cos(Θ -φ)cosΘ
= 1.001146[3-35]

By the way, the value of ratios g'a, g'b does not concord g'. I canestimate them. As I got solutions [3-34] and [3-35], I can understandwhat only compare cosine ingredient o-a, o-b of P and Pʼ that has acurvature is insufficient. Therefore, I make o-c as the cosine ingredient of
P' on dimension rj that is dimension xj have a curvature and work in thecomparison with o-a, pictured them in [Fig.12]. However, cannot pursue
only- １９ -


PP' =φ・・

φ=1.000000232
sinφ[3-36]

in my current. In this reason, I do not find the logical limitation that
determines space curvature Φ.
However, I can expect that error k has


oc
k= ＿
ob

・・・・

= 1.000011657(= 1.00001363 )[3-37]

from the existence of solution [3-36].
Directionality in the future

In the above, light velocity c, Planck's constant , electric charge q,
electronic mass mq and all physical quantity to have gotten from the gap
space theory are found by the space which has curvature Φ.
After all, space curvature Φ is the principle of the force and invents
gravitation. Yes, space curvature Φ is gravitation itself.
I do not find how much value the cosmological term of the generalrelativity. However, I look forward to the gap space theory do notcontradict to it.
If the gap space theory is right, we have the following propositions.
① The “generalization of mass” and the “theoretical evidence withexperiment value”.
② “Unification of the interaction” and “Theoretical prove the force exists”③ “Find the gravitational constant”
Already, we got the way that we should advance on discussed ①, ② in the<< Pair production of light velocity c with Planck’s constant  >>. We will
be able to solve ③ in the near future.

- ２０ -

[VAMS] unit system
Physical quantity
LengthTime
Mass
Momentum
Force
EnergyAngular momentum
PowerElectric charge, Electric flux
Magnetic flux, Magnetic charge
Electric potential, Magnetic current
Electric current, Magnetic potential
Electric current density
Density of electric charge
Electric displacement
Flux density
Electric field
Magnetic field
Dielectric constant
Magnetic permeability
Electric resistance
ConductanceElectric conductivity
Electric capacity
InductanceElectric moment
Magnetic moment
Electric polarization
Magnetic polarization

Power of Dimention[VAMS] unit system[SI] unit system
V
A
m
s
A
Kg
m
s
m
0
0
1
0
0
0
1
0
s
0
0
0
1
0
0
0
1
Kg
1
1
-2
3
0
1
0
0
N・s
1
1
-1
2
0
1
1
-1
N
1
1
-1
1
0
1
1
-2
J
1
1
0
1
0
1
2
-2
J・s
1
1
0
2
0
1
2
-1
P
1
1
0
0
0
1
2
-3
C
0
1
0
1
1
0
0
1
wb
1
0
0
1
-1
1
2
-2
V
1
0
0
0
-1
1
2
-3
A
0
1
0
0
1
0
0
0
A/Am2
0
1
-2
0
1
0
-2
0
C/m3
0
1
-3
1
1
0
-3
1
C/m2
0
1
-2
1
1
0
-2
1
T
1
0
-2
1
-1
1
0
-2
V/m
1
0
-1
0
-1
1
1
-3
A/m
0
1
-1
0
1
0
-1
0
F/m
-1
1
-1
1
2
-1
-3
4
H/m
1
-1
-1
1
-2
1
1
-2
Ω
1
-1
0
0
-2
1
2
-3
S
-1
1
0
0
2
-1
-2
3
1/(Ω・m) -1
1
-1
0
2
-1
-3
3
F
-1
1
0
1
2
-1
-2
4
H
1
-1
0
1
-2
1
2
-2
C・m
0
1
1
1
1
0
1
1
Wb・m
1
0
1
1
-1
1
3
-2
C/m2
0
1
-2
1
1
0
-2
1
Wb/m2
1
0
-2
1
-1
1
0
-2
Unit

[VAMS] 単位系
物理量
長さ
時間
質量
運動量
力
エネルギー
角運動量
仕事率
電荷、電束
磁束、磁荷
電位、磁流
電流、磁位
電流密度
電荷密度
電束密度
磁束密度
電場
磁場
誘電率
透磁率
電気抵抗
コンダクタンス
電気伝導度
電気容量
インダクタンス
電気モーメント
磁気モーメント
電気分極
磁気分極

基本単位ベキ[VAMS]単位系[SI]単位系
V
A
m
s
A
Kg
m
m
0
0
1
0
0
0
1
s
0
0
0
1
0
0
0
Kg
1
1
-2
3
0
1
0
N・s
1
1
-1
2
0
1
1
N
1
1
-1
1
0
1
1
J
1
1
0
1
0
1
2
J・s
1
1
0
2
0
1
2
P
1
1
0
0
0
1
2
C
0
1
0
1
1
0
0
wb
1
0
0
1
-1
1
2
V
1
0
0
0
-1
1
2
A
0
1
0
0
1
0
0
2
A/Am
0
1
-2
0
1
0
-2
C/m3
0
1
-3
1
1
0
-3
C/m2
0
1
-2
1
1
0
-2
T
1
0
-2
1
-1
1
0
V/m
1
0
-1
0
-1
1
1
A/m
0
1
-1
0
1
0
-1
F/m
-1
1
-1
1
2
-1
-3
H/m
1
-1
-1
1
-2
1
1
Ω
1
-1
0
0
-2
1
2
S
-1
1
0
0
2
-1
-2
1/(Ω・m) -1
1
-1
0
2
-1
-3
F
-1
1
0
1
2
-1
-2
H
1
-1
0
1
-2
1
2
C・m
0
1
1
1
1
0
1
Wb・m
1
0
1
1
-1
1
3
2
C/m
0
1
-2
1
1
0
-2
2
Wb/m
1
0
-2
1
-1
1
0
単位

s
0
1
0
-1
-2
-2
-1
-3
1
-2
-3
0
0
1
1
-2
-3
0
4
-2
-3
3
3
4
-2
1
-2
1
-2

GAPS T. Sheet 1 (ωτ= Θe)wτ=ωτ/sinθθvalue of [ wτ][ real part ]R ωexp(±iρ)cosδ= [ imaginary part ]θ=asin(ωτ/wτ) R wsinθcos(wτcosθ)cos(wτsinθ)R ωexp(±iρ)cosδ= cωexp(+ρ)cosδ=i R wsinθsin(wτcosθ)cos(wτsinθ)ωexp(-ρ)cosδ=/ccwsinθexp(wτcosθ)cos(wτsinθ)

wsinθexp(-wτcosθ)cos(wτsinθ)00#DIV/0!

#DIV/0!

#DIV/0!

#DIV/0!

#DIV/0!

#DIV/0!

0.001

0.001

#NUM!

#NUM!

#NUM!

#NUM!

#NUM!

#NUM!

0.001001

0.001001

#NUM!

#NUM!

#NUM!

#NUM!

#NUM!

#NUM!

0.001005

0.001005

#NUM!

#NUM!

#NUM!

#NUM!

#NUM!

#NUM!

0.00101

0.00101

#NUM!

#NUM!

#NUM!

#NUM!

#NUM!

#NUM!

0.001020.00102

#NUM!

#NUM!

#NUM!

#NUM!

#NUM!

#NUM!

0.00105

0.00105

#NUM!

#NUM!

#NUM!

#NUM!

#NUM!

#NUM!

0.00110.0011

#NUM!

#NUM!

#NUM!

#NUM!

#NUM!

#NUM!

0.00120.0012

#NUM!

#NUM!

#NUM!

#NUM!

#NUM!

#NUM!

0.00150.0015

#NUM!

#NUM!

#NUM!

#NUM!

#NUM!

#NUM!

0.002

0.002

#NUM!

#NUM!

#NUM!

#NUM!

#NUM!

#NUM!

0.003

0.003

#NUM!

#NUM!

#NUM!

#NUM!

#NUM!

#NUM!

0.004

0.004

#NUM!

#NUM!

#NUM!

#NUM!

#NUM!

#NUM!

0.005

0.005

#NUM!

#NUM!

#NUM!

#NUM!

#NUM!

#NUM!

0.01

0.01

#NUM!

#NUM!

#NUM!

#NUM!

#NUM!

#NUM!

0.05

0.05

#NUM!

#NUM!

#NUM!

#NUM!

#NUM!

#NUM!

π/32

0.09817477

#NUM!

#NUM!

#NUM!

#NUM!

#NUM!

#NUM!

π/16

0.196349541

#NUM!

#NUM!

#NUM!

#NUM!

#NUM!

#NUM!

π/8

0.392699082

#NUM!

#NUM!

#NUM!

#NUM!

#NUM!

#NUM!

π/4

0.785398163

#NUM!

#NUM!

#NUM!

#NUM!

#NUM!

Θ

0.955316618

1.570796327

0.577350269

3.37867E-17

0.577350269

0.577350269

Θ'

0.955316618

1.570796285

0.577350269

2.32462E-08

0.577350292

0.577350246 0.999999919

0.96

1.471978367

0.571958749

0.054333298

0.63160841

0.522616408

0.97

1.396578918

0.560592186

0.095154844

0.672722699

0.480611169 0.714426865

0.98

1.345880466

0.549419179

0.122032563

0.700296097

0.452313503 0.645888938

0.99

1.305314832

0.538434371

0.143091124

0.722369803

0.429678317 0.594817661

111.270729093

0.527632619

0.16066663

0.741237521

0.410408187 0.553679725

π/3

1.047197551

1.148768441

0.478978107

0.219057481

0.808809151

0.342981044 0.424056829

1.07

1.103566123

0.456755146

0.238921505

0.834658096

0.318344422 0.381406978

1.1

1.052106942

0.42868808

0.260076352

0.865011729

0.290647133

1.12

1.021632472

0.41067342

0.271774998

0.883612936

0.274457624 0.310608427
0.252841727 0.277919978

B

π/2

#NUM!
1
0.82743738

0.33600369

1.15

0.980382018

0.384633258

0.286502499

0.909764489

1.170019129

0.955316618

0.36787825

0.294767392

0.926327125

0.239896054 0.258975526

1.27

0.851421497

0.290900989

0.3224704

1.002789845

0.188085814 0.187562544

1.351

0.785414239

0.235716287

0.333331452

1.061223242

0.157056516 0.147995737

1.37

0.771639616

0.223593362

0.334794073

1.074809295

0.150799834 0.140303805

1.47

0.70742029

0.164395223

0.337273614

1.146804193

0.122757905 0.107043474

1.52

0.679620352

0.1374606

0.335819001

1.183580736

0.11124701 0.093991906

1.570796327

0.653757546

0.11174974

0.332871812

1.221773346

0.100912046 0.082594735

1.6

0.639847215

0.097680322

0.330591236

1.244180345

0.095510278 0.076765622

1.67

0.608997992

0.065946825

0.323619909

1.29943283

0.083943415 0.064600042

1.77

0.570112671

0.025131944

0.310596354

1.38272882

0.070224695 0.050787034

1.87

0.536190121-0.010842846

0.294748388

1.471981573

0.059100047 0.040149991

1.97

0.506285747-0.042412154

0.276744742

1.568021604

0.049990665 0.031881363

2π/3

2.094395102

0.473641685-0.076069727

0.2521209

1.698161648

0.040839193 0.024049061

3π/42.35619449

0.417469923-0.128879952

0.195413014

2.017325515

0.027162839 0.013464777

2.38590.411954356-0.133470697

0.188748189

2.057930171

0.025967988 0.012618498

2.4

0.409388671-0.135556398

0.185576642

2.077545318

0.025421456 0.012236294

2.5

0.392096497-0.148677051

0.16299916

2.223239969

0.021893089

2.6

0.376243647-0.158999886

0.140429725

2.381197626

0.018898671 0.007936624
0.016348552 0.006404905

0.00984738

2.7

0.361653193-0.166702249

0.118068284

2.55250487

7π/8

2.748893572

0.354933152-0.169565878

0.107265607

2.641474223

0.01524092 0.005769854

15π/162.945243113

0.330334194-0.175553741

0.065195922

3.036773569

0.011548317 0.003802825

31π/32

3.043417883

0.319293633-0.175504095

0.045187092

3.259571628

0.010076036 0.003091215

π3.141592654

0.308979608-0.173625234

0.026022873

3.501081834

0.008803825 0.002514601

33π/32

3.239767424

0.299321533-0.170065299

0.007807352

3.762925654

0.007702294

17π/16

3.337942194

0.29025782-0.164971464-0.009367861

4.046868465

0.006746782 0.001667161

9π/8

3.534291735

0.2737039-0.150766461-0.040291189

4.688913737

0.005193933 0.001107705

3.6

0.268583229-0.144974936-0.049550558

4.928229168

0.004762966 0.000966466

3.7

0.261152019-0.13531384-0.062541908

5.318510742

0.00417811 0.000785579

3.8

0.25412552-0.124762882-0.074171384

5.742747004

0.003668483 0.000638803

5π/4

3.926990817

0.245735071-0.11031313-0.0869349

6.335236416

0.003113801 0.000491505

4π/3

4.188790205

0.230089887-0.077998663-0.106085326

7.775422869

0.002229832

4.20680.229087204-0.075697911-0.107049432

7.886659347

0.002179599 0.000276365

0.00204689

0.00028678

3π/2

4.71238898

0.204139377-0.011434267-0.116483173

11.81448683

0.001159515 9.81435E-05

5π/35.235987756

0.183479772

0.044458789-0.095496934

18.12924374

0.000612063 3.37611E-05

5.412810.177421162

0.05882824-0.083200706

20.9901511

0.000494666 2.35666E-05

7π/4

5.497787144

0.174650375

0.064764713-0.076616945

22.52863045

0.000446748 1.98302E-05

5.59

0.171740424

0.070461207-0.069069013

24.33137442

0.000400113 1.64443E-05

5.69

0.168692911

0.07574004-0.060494407

26.45650201

0.000355154 1.34241E-05

5.79

0.165752166

0.080068211-0.051608598

28.77464002

0.00031536 1.09596E-05

15π/8

5.890486225

0.162899082

0.083452559-0.042462648

31.31654202

0.000279961 8.93971E-06

31π/166.086835766

0.157599577

0.08728783-0.024325395

36.97543785

0.000222063

63π/326.185010537

0.15507758

0.087853732-0.015297634

40.19088881

0.000197863 4.92308E-06
0.000176351 4.03594E-06

6.0057E-06

2π6.283185307

0.152635344

0.087548167-0.006406743

43.69528591

2.05π

6.44026494

0.148884421

0.085325973

0.007341745

49.97031462

0.000146776 2.93726E-06

2.1π

6.597344573

0.145314075

0.081113154

0.020247931

57.17552186

0.000122243 2.13803E-06

2.15π

6.754424205

0.141911529

0.075105317

0.032050103

65.45145129

0.000101877 1.55653E-06

2.2π

6.911503838

0.138665188

0.067528748

0.042523387

74.96018288

8.49567E-05 1.13336E-06

2.25π

7.068583471

0.135564502

0.058634351

0.051482903

85.88866858

7.0888E-05 8.25348E-07

7.30130.131218223

0.043612115

0.061680836

105.157731

5.42665E-05 5.16049E-07

2.35π

7.382742736

0.129762463

0.037980578

0.064333574

112.9008143

4.94357E-05 4.37869E-07

2.4π

7.539822369

0.12704428

0.02678841

0.068070413

129.5205604

4.13154E-05 3.18988E-07

2.45π

7.696902001

0.124437931

0.015399927

0.069984674

148.643357

3.45459E-05 2.32408E-07

2.5π

7.853981634

0.121936635

0.004092991

0.070106443

170.6519487

2.8899E-05 1.69345E-07

2.55π

8.011061267

0.119534151-0.006867597

0.06850547

195.9882794

2.4186E-05 1.23405E-07

2.6π

8.168140899

0.117224724-0.017235414

0.065288152

225.1627324

2.02503E-05 8.99361E-08

2.65π8.325220532

0.115003039-0.026787173

0.060593832

258.7648218

1.6962E-05 6.55498E-08

8.52320.112320287-0.037363085

0.052835854

308.4878162

1.35747E-05

8.639379797

0.110803582-0.042688954

0.047470097

342.0818142

1.19146E-05 3.48296E-08
9.99127E-06 2.53912E-08

2.75π

4.4004E-08

2.8π8.79645943

0.108817027-0.04874138

0.039443272

393.4928192

2.85π

8.953539063

0.106900585-0.053386984

0.030734129

452.75944

8.3814E-06 1.85118E-08

2.9π9.110618695

0.105050601-0.056564692

0.021574678

521.0963633

7.03331E-06 1.34971E-08

2.95π

9.267698328

0.103263671-0.058249649

0.012199349

599.90784

5.90398E-06 9.84148E-09

3π9.424777961

0.10153662-0.058452584

0.002839608

690.81749

4.95756E-06 7.17636E-09
4.16412E-06 5.23326E-09

3.05π

9.581857593

0.099866482-0.05721842-0.006281191

795.7028214

3.1π

9.738937226

0.098250487-0.05462415-0.014952632

916.7352144

3.4987E-06 3.81648E-09

3.15π

9.896016859

0.096686037-0.050776082-0.022981623

1056.42624

2.94045E-06 2.78339E-09

3.2π

10.05309649

0.095170704-0.045806497-0.030196272

1217.681323

2.47195E-06 2.03005E-09

3.25π

10.21017612

0.093702205-0.039869825-0.036449178

1403.861914

2.07866E-06 1.48067E-09

10.42394

0.091775182-0.030549776-0.04320184

1704.365778

1.64266E-06 9.63794E-103.35π

10.52433539

0.090897275-0.025798143-0.045617803

1867.169263

1.47096E-06 7.87801E-103.4π10.68141502

0.089556938-0.018043525-0.048381537

2154.006498

1.23785E-06 5.74674E-10

3.45π

10.83849465

0.088255606-0.010073182-0.049881336

2485.399101

1.04193E-06 4.19221E-10

3.5π10.99557429

0.086991598-0.00208503-0.050117948

2868.327393

8.77221E-07

3.55π

11.15265392

0.08576333

0.005728269-0.049121935

3310.872852

7.38711E-07 2.23117E-10

3.6π

11.30973355

0.084569305

0.01318363-0.046952135

3822.392817

6.22205E-07 1.62779E-103.65π

11.46681319

0.083408108

0.020111541-0.043693525

4413.723055

5.24183E-07 1.18762E-10

11.65030.082091486

0.02733358-0.038654512

5222.417795

4.29168E-07 8.21781E-11
3.83305E-07 6.67259E-11

3.0583E-10

11.75410.081364928

0.030928415-0.035289067

5744.471506

3.75π

11.78097245

0.081178925

0.031795811-0.034363904

5887.996276

3.72258E-07 6.32231E-113.8π11.93805208

0.080108476

0.036310738-0.028567132

6802.310245

3.13798E-07 4.61311E-11

3.85π

12.09513172

0.079065918

0.039819866-0.022222649

7859.858653

2.64568E-07 3.36607E-113.9π

12.25221135

0.078050175

0.042264746-0.01549778

9083.238375

2.23102E-07

3.95π

12.40929098

0.077060226

0.043613746-0.008564593

10498.63191

1.88168E-07 1.79231E-11

2.4562E-114π12.56637061

0.076095097

0.04386212-0.00159575

12136.37915

1.58732E-07

4.05π

12.72345025

0.075153868

0.043031458

0.005239566

14031.64064

1.33923E-07 9.54436E-12

1.3079E-114.1π

12.88052988

0.074235659

0.041168533

0.011779541

16225.1672

1.1301E-07

4.15π

13.03760951

0.073339637

0.038343599

0.01787336

18764.1928

9.53779E-08 5.08297E-12

6.9651E-12

4.2π

13.19468915

0.072465005

0.034648171

0.0233845

21703.4707

8.05093E-08 3.70951E-12

4.25π

13.35176878

0.071611007

0.03019237

0.028193609

25106.47578

6.79689E-08 2.70722E-12

13.55537

0.070533611

0.02349245

0.033221779

30329.12287

5.45872E-08 1.79983E-124.35π

13.66592804

0.069962054

0.019514667

0.035328183

33609.77136

4.84652E-08

4.4π

13.82300768

0.069165753

0.013577351

0.037519969

38894.33445

4.09338E-08 1.05244E-12

1.442E-12

4.45π

13.98008731

0.068387389

0.007441626

0.038744527

45015.23128

3.45775E-08

4.5π

14.13716694

0.067626362

0.001260514

0.038993977

52105.53437

2.92122E-08 5.60636E-13

7.6813E-13

4.55π

14.29424657

0.066882099-0.004815281

0.038283976

60319.58666

2.46827E-08 4.09199E-134.6π

14.45132621

0.066154051-0.010640899

0.036652839

69836.41484

2.08582E-08 2.98672E-134.65π

14.60840584

0.065441695-0.016080633

0.034160138

80863.69218

1.76285E-08 2.18002E-13

14.78352

0.064665434-0.021539352

0.030462884

95233.74315

1.46159E-08 1.53474E-13

4.75π

14.9225651

0.064062067-0.025323217

0.026922985

108451.8693

1.25965E-08 1.16148E-13

4.8π

15.07964474

0.063393853-0.028925875

0.022385124

125616.5871

1.06499E-08 8.47807E-14

4.85π

15.23672437

0.062739445-0.031746363

0.017393306

145512.799

9.00511E-09 6.18853E-14

4.9π

15.393804

0.062098418-0.03373241

0.01207798

168577.1774

7.61522E-09 4.51735E-14
6.44057E-09 3.29751E-14

4.95π

15.55088364

0.061470366-0.034852875

0.006574708

195316.4792

5π15.70796327

0.060854899-0.035098068

0.001020828

226318.8325

5.4477E-09 2.40709E-14

5.05π

15.8650429

0.060251641-0.034479556-0.004447853

262266.847

4.60837E-09 1.75713E-14
3.89877E-09 1.28269E-14

5.1π

16.02212253

0.059660233-0.033029465-0.009700273

303952.8426

5.15π

16.17920217

0.05908033-0.030799316-0.01461315

352296.54

3.29876E-09 9.36359E-15

5.2π

16.3362818

0.058511597-0.02785842-0.019073779

408365.6119

2.79137E-09 6.83547E-15

5.25π

16.49336143

0.057953716-0.024291877-0.022982522

473399.5587

2.36226E-09 4.98999E-15

16.69062

0.057268034-0.019079504-0.026981238

570000.481

1.91581E-09 3.36107E-15

5.35π

16.8075207

0.056869289-0.015686934-0.028823551

636350.1479

1.69227E-09 2.65934E-15

5.4π

16.96460033

0.056342161-0.010875373-0.030639083

737877.7701

1.43252E-09 1.94141E-15

5.45π

17.12167996

0.05582472-0.005886064-0.031671365

855673.1932

1.21275E-09 1.41731E-15

5.5π

17.27875959

0.055316702-0.000843544-0.03190968

992352.6274

1.02679E-09

1.0347E-15

5.55π

17.43583923

0.054817851

0.004128629-0.03136267

1150954.381

8.6942E-10

7.5539E-165.6π

17.59291886

0.054327922

0.008910826-0.030057788

1335007.153

7.36231E-10 5.51481E-16

5.65π

17.74999849

0.053846676

0.013390147-0.0280403

1548609.412

6.23498E-10 4.02618E-16

17.9197

0.053336256

0.017769775-0.025131421

1818092.052

5.2107E-10 2.86603E-16

5.75π

18.06415776

0.05290933

0.021037463-0.022128875

2084273.557

4.47284E-10 2.14599E-16
3.78887E-10 1.56676E-16

5.8π

18.22123739

0.052452794

0.024035225-0.018400156

2418288.769

5.85π

18.37831702

0.052004074

0.026393292-0.014284828

2806029.628

3.20974E-10 1.14387E-16

5.9π

18.53539666

0.051562968

0.028065217-0.009889643

3256165.65

2.71934E-10 8.35135E-17

5.95π

18.69247629

0.051129287

0.029021934-0.005326313

3778769.3

2.30404E-10 6.09732E-17

6π18.84955592

0.050702842

0.029252174-0.000708738

4385543.592

1.95231E-10 4.45168E-17

6.05π

19.00663555

0.050283455

0.028762438

0.003849768

5090086.709

1.65439E-10 3.25022E-17

6.1π

19.16371519

0.049870952

0.027576545

0.008239197

5908199.655

1.40203E-10 2.37303E-17

6.15π

19.32079482

0.049465165

0.025734782

0.012355439

6858243.967

1.18826E-10

6.2π

19.47787445

0.049065931

0.023292659

0.016102695

7961557.633

1.00715E-10 1.26501E-17

6.25π

19.63495408

0.048673092

0.020319335

0.019395648

9242938.727

8.53697E-11

19.82787

0.048199157

0.016060841

0.022712026

11103108.7

6.9691E-11 6.27671E-18

1.7326E-17
9.2362E-18

6.35π

19.94911335

0.047905995

0.013112387

0.02434081

12459861.77

6.13498E-11 4.92379E-18

6.4π

20.10619298

0.047531446

0.009067144

0.025890141

14467834.61

5.20128E-11 3.59506E-18

6.45π

20.26327262

0.047162711

0.004862657

0.026781438

16800381.65

4.40996E-11 2.62492E-18

6.5π

20.42035225

0.046799655

0.000603846

0.02700318

19510108.24

3.73927E-11 1.91658E-18

6.55π

20.57743188

0.046442147-0.003604661

0.026560259

22658166.11

3.17078E-11

6.6π

20.73451151

0.046090062-0.007661059

0.025473611

26315644.78

2.68888E-11 1.02178E-18

6.65π

20.89159115

0.045743278-0.011468776

0.023779473

30565190.01

2.28036E-11 7.46064E-19

21.05754

0.045382539-0.015122898

0.021385783

35804410.45

1.91612E-11 5.35162E-19

1.3994E-18

6.75π

21.20575041

0.045065137-0.017991348

0.018783204

41240446.32

1.64037E-11 3.97758E-19

6.8π

21.36283004

0.044733554-0.020558395

0.01561851

47907758.8

1.39139E-11 2.90432E-19

6.85π

21.51990968

0.044406816-0.022584405

0.012117527

55655850.9

1.18027E-11 2.12066E-196.9π

21.67698931

0.044084818-0.024027864

0.008370538

64660335.65

6.95π

21.83406894

0.043767458-0.024862006

0.00447249

75125422.06

1.00124E-11 1.54846E-19
8.4941E-12 1.13066E-19

7π21.99114858

0.043454635-0.025075246

0.00052063

87288580.56

7.20643E-12 8.25587E-20

7.05π

22.14822821

0.043146254-0.024671247-0.003387875

101425970.9

6.11429E-12 6.02833E-20

7.1π22.30530784

0.042842221-0.023668613-0.007158293

117858757.7

5.18794E-12 4.40183E-20

7.15π

22.46238747

0.042542443-0.02210023-0.010700582

136960457.8

4.40217E-12 3.21419E-20

7.2π

22.61946711

0.042246833-0.020012272-0.013931501

159165490.7

3.73559E-12 2.34699E-20

7.25π

22.77654674

0.041955304-0.017462898-0.016776537

184979125.9

3.17011E-12 1.71377E-20

22.96632

0.041608422-0.013865917-0.019608425

221824065.6

2.60005E-12 1.17212E-20

7.35π

23.090706

0.041384155-0.011262791-0.021064341

249878884.7

2.28333E-12 9.13776E-21

7.4π

23.24778564

0.041104374-0.007773043-0.022415453

290443766.1

1.93797E-12 6.67246E-21

7.45π

23.40486527

0.040828352-0.004139743-0.023199252

337608682.7

1.64493E-127.5π

23.5619449

0.040556013-0.000453503-0.023404214

392449656.3

1.39626E-12 3.55781E-21

4.8723E-21

7.55π

23.71902453

0.040287285

0.003194983-0.023033046

456218457.2

1.18524E-12 2.59797E-21

7.6π

23.87610417

0.040022095

0.006717145-0.022102435

530371358.5

1.00616E-12 1.89708E-21

7.65π

24.0331838

0.039760374

0.010028649-0.020642456

616602600.2

8.54172E-13 1.38529E-21

24.19632

0.039492162

0.013161175-0.018611561

721061242.5

7.20614E-13

24.34734307

0.039247071

0.015715308-0.016315935

833506983.9

6.15688E-13 7.38672E-227.75π

9.9938E-22

7.8π

24.5044227

0.03899536

0.017959973-0.01356694

969141959.1

5.22754E-13 5.39398E-22

7.85π

24.66150233

0.038746857

0.019735937-0.010520552

1126893128

4.43866E-13 3.93884E-227.9π

24.81858196

0.038501502

0.021005794-0.007254958

1310373284

3.76899E-13 2.87627E-22

7.95π

24.9756616

0.038259235

0.021744926-0.00385269

1523786374

3.20048E-13 2.10035E-228π25.13274123

0.038020.021941949-0.00039857

1772024374

2.71784E-13 1.53375E-228.1π

25.44690049

0.037550395

0.020730629

0.006326995

2396678315

1.96017E-138.2π

25.76105976

0.037092252

0.017541568

0.012275782

3242004554

1.41394E-13 4.36133E-238.3π26.10557

0.036602532

0.012197659

0.017251072

4516111813

9.88422E-14 2.18866E-23

8.4π

26.38937829

0.036208712

0.006801468

0.019762912

5934809792

7.36052E-14 1.24023E-238.5π26.70353756

0.035782544

0.000353046

0.020651636

8031436594

5.31181E-14 6.61377E-24

8.6π

27.01769682

0.035366293-0.00597952

0.01951913

10870204665

3.83388E-14 3.52697E-24

27.33569

0.034954713-0.01164878

0.01647475

14768762068

2.75657E-14 1.86649E-248.8π27.64601535

0.03456219-0.015944503

0.011991495

19920288718

1.99808E-14 1.00304E-24

8.9π

27.96017462

0.034173699-0.018658869

0.006401223

26971589654

1.44274E-149π28.27433388

0.033793846-0.019504631

0.000314899

36523340945

1.04188E-14 2.85264E-25

9.1π

28.58849315

0.033422346-0.018441394-0.005668106

49463670139

7.52497E-15 1.52131E-25

9.2π28.90265241

0.033058926-0.015613761-0.010971568

66996628462

5.43557E-15

29.24528

0.03267148-0.010888213-0.015398987

93286012501

3.81281E-15 4.08723E-26

9.4π

29.53097094

0.032355296-0.006045381-0.017671635

1.22952E+11

2.83716E-15 2.30754E-26

9.5π

29.84513021

0.032014597-0.000282617-0.018478318

1.66589E+112.05012E-15 1.23065E-26

9.6π

30.15928947

0.031681

0.005387434-0.017476428

2.25739E+11

1.48158E-15 6.56325E-27

30.47561

0.03135206

0.010449319-0.014776838

3.06563E+11

1.06844E-15 3.48522E-27

9.8π30.78760801

0.031034239

0.014335643-0.010743724

4.1463E+11

7.74036E-16 1.86681E-27

9.9π

31.10176727

0.030720663

0.016783606-0.005726953

5.62023E+11

5.59563E-16 9.95623E-28

10π31.41592654

0.030413361

0.017554602-0.000255057

7.61887E+11

4.0456E-16 5.30997E-28≒10.3π32.38531

0.029502735

0.009833186

0.013905446

1.9493E+12

1.48798E-16 7.63341E-29
8.00396E-17 2.29147E-29

8.1787E-23

5.3491E-25

8.1132E-26

10.5π

32.98672286

0.02896469

0.00023134

0.016718833

3.49293E+12≒10.7π33.6158

0.028422505-0.009473164

0.013396502

6.43137E+12

4.18585E-17 6.50849E-30

11π34.55751919

0.02764777-0.015959022

0.000210784

1.6049E+13

1.58723E-17≒11.3π35.52566

0.026894132-0.008963919-0.012676283

4.1121E+13

5.86173E-18 1.42548E-31

9.8899E-31

11.5π

36.12831552

0.026445406-0.00019285-0.015265265

7.38892E+13

3.15426E-18

4.2689E-32≒11.7π36.75624

0.025993524

0.008663876-0.012251842

1.36112E+14

1.65431E-18

1.2154E-32

12π37.69911184

0.025343273

0.014629307-0.000177112

3.40811E+14

6.28054E-19 1.84282E-33≒12.3π38.66621

0.02470927

0.008235838

0.011646698

8.7428E+14

2.32734E-19

12.5π

39.26990817

0.024329338

0.000163225

0.014044216

1.57465E+15

1.25277E-19 7.95583E-35

2.662E-34≒12.7π39.8968

0.023946981-0.007981261

0.011287851

2.90162E+15

6.58653E-20 2.26995E-35

13π40.8407045

0.02339342-0.013504122

0.000150909

7.28674E+15

2.50296E-20 3.43495E-36≒13.3π41.80691

0.022852676-0.00761719-0.010771709

1.87115E+16

9.30185E-2113.5π

42.41150082

0.022526848-0.000139936-0.013004029

3.37684E+16

5.00836E-21 1.48315E-37≒13.7π4.9712E-37

43.0376

0.022199079

0.007399247-0.010463772

6.2248E+16

2.63847E-21 4.23864E-38

43.288296

0.022070496

0.009707743-0.008252412

7.95254E+16

2.04139E-21 2.56697E-38

14π43.98229715

0.021722189

0.01253965-0.000130118

1.56701E+17

1.00357E-21 6.40435E-39≒14.3π44.94779

0.021255518

0.007084409

0.010019356

4.0276E+17

3.73861E-22 9.28249E-40

14.5π

45.55309348

0.020973036

0.000121299

0.012107293

7.28073E+17

2.01355E-22 2.76559E-40≒14.7π46.17848

0.020688961-0.006896064

0.009752007

1.3425E+18

1.06262E-22 7.91527E-41

15π47.1238898

0.020273837-0.011703755

0.000113346

3.38676E+18

4.04488E-23 1.19432E-41≒15.3π48.08867

0.019867039-0.006622158-0.009364621

8.71097E+18

1.51015E-23 1.73362E-4215.5π

48.69468613

0.019619757-0.000106151-0.011326248

1.57713E+19

8.1347E-24/c ; Planck's c./light v.

48.886015

0.01954296

0.002042012-0.011096084

1.90228E+19

6.6916E-24 3.51767E-43

5.1579E-43≒15.7π49.31939

0.019371212

0.006456403-0.009131293

2.90864E+19

4.2998E-24 1.47829E-43

16π50.26548246

0.019006565

0.010972332-9.96196E-05

7.35183E+19

1.63771E-24 2.22763E-44≒16.3π51.22968

0.018648799

0.006216144

0.00879045

1.89219E+20

6.12585E-25 3.23745E-45

16.5π

51.83627878

0.018430542

9.36731E-05

0.010639864

3.43036E+20

3.3004E-25 9.62115E-46≒16.7π52.460448

0.018211233-0.006069994

0.00858444

6.3279E+20

1.74683E-25 2.76051E-46

17π53.40707511

0.017888408-0.01032695

8.82436E-05

1.60205E+21

6.65734E-26 4.15552E-47≒17.3π54.37081

0.017571299-0.005856592-0.00828291

4.1259E+21

2.49415E-26 6.04512E-48

17.5π

54.97787144

0.017377259-8.32728E-05-0.010031915

7.48825E+21

1.34406E-26 1.79489E-48≒17.7π55.60159

0.017182308

0.005727408-0.008099239

1.38165E+22

7.12197E-27 5.15468E-49

18π

56.54866776

0.016894511

0.009753269-7.87105E-05

3.50295E+22

2.71578E-27 7.75284E-50≒18.3π57.51189

0.016611531

0.005537151

0.007830229

9.02567E+22

1.01901E-27 1.12901E-50

18.5π

58.11946409

0.01643786

7.45132E-05

0.009489683

1.6399E+23

5.49177E-28 3.34884E-51≒18.7π58.74269

0.016263449-0.005420739

0.007666446

3.02611E+23

2.91327E-28

19π59.69026042

0.016005248-0.00923997

7.06428E-05

7.6827E+23

1.11135E-28 1.44657E-52≒19.3π60.65307

0.015751159-0.005250398-0.007424698

1.98043E+24

4.17549E-29 2.10838E-53

19.5π

61.26105675

0.015594823-6.70664E-05-0.009003061

3.60169E+24

2.2506E-29 6.24874E-54≒19.7π61.88388

0.015437858

0.005145525-0.007277345

6.64713E+24

1.19504E-29 1.79784E-54

20π62.83185307

0.015204922

0.008777996-6.37548E-05

1.68958E+25

4.56073E-30 2.69932E-55

628.3185307

0.001520434

0.000877823-6.37517E-07

6.5821E+269

1.1707E-276

3.02169E+25

3.16153E-26

0.961835πE+25

#NUM!

#NUM!

#NUM!

Graph.1

Graph.2

Graph.30Graph.4

9.6271E-52

0
#NUM!

Sheet2ωτwτ

ωτ= wτsinθ

value of [ωτ]0θ[M τsinθ]ωτsinθexp(-ρ)cosδ=[v]wτsin2θexp(-wτcosθ)cos(wτsinθ)θ=asin(ωτ/wτ)cω2exp(+ρ)cosδ/(σ 2+ω2)=[ ]csin2θexp(wτcosθ)cos(wτsinθ)ω2exp(-ρ)cosδ/(σ 2+ω2)=

ratio/c=3.51767E-43

sin2θexp(-wτcosθ)cos(wτsinθ)[QR] Qω2exp(-iρ)cosδ/(σ 2+ω2)=#DIV/0!

eiectron[Q I]

Qsin2θcos(wτcosθ)cos(wτsinθ) -i Qsin2θsin(wτcosθ)cos(wτsinθ)q = M τsinθ/Q R

048.8766796

0

0

0

0

0

0

π/2×0.00000000000553261063

8.6906E-12

48.8766796

1.77807E-13

9.16486E-46

5.33051E-05

1.8751E-47

3.51767E-43

5.72206E-27

3.10931E-26

π/2×0.0000000292757

4.59862E-08

48.8766796

9.40861E-10

2.56614E-38

1492.530397

5.25023E-40

3.51767E-43

1.60216E-19

8.706E-19

π/2×0.00001312066853

2.06099E-05

48.87668

4.21671E-07

5.15439E-33

299792458

1.05457E-34

3.51767E-43

3.21814E-14

1.7487E-13

1.60167E-19

0.001

0.001

48.8766801

2.04597E-05

1.21346E-29

7.05779E+112.4827E-31

3.51767E-43

7.57623E-11

4.11684E-10

1.60167E-19

0.001001

0.001001

48.8766801

2.04801E-05

1.21589E-29

7.07191E+11

2.48767E-31

3.51767E-43

7.59139E-11

4.12508E-10

1.60167E-19

0.001005

0.001005

48.8766801

2.0562E-05

1.22563E-29

7.12855E+11

2.50759E-31

3.51767E-43

7.65218E-11

4.15811E-10

1.60167E-19

0.00101

0.00101

48.8766801

2.06643E-05

1.23785E-29

7.19965E+11

2.5326E-31

3.51767E-43

7.72851E-11

4.19959E-100.001020.0010248.8766801

2.08688E-05

1.26248E-29

7.34293E+11

2.583E-31

3.51767E-43

7.88231E-11

4.28316E-10

1.60167E-19

0.00105

0.00105

48.87668011

2.14826E-05

1.33784E-29

7.78122E+11

2.73717E-31

3.51767E-43

8.3528E-11

4.53882E-10

1.60167E-19

0.00110.001148.87668011

2.25056E-05

1.46829E-29

8.53993E+11

3.00406E-31

3.51767E-43

9.16724E-11

4.98138E-10

1.60167E-19

0.00120.001248.87668012

2.45516E-05

1.74738E-29

1.01632E+12

3.57508E-31

3.51767E-43

1.09098E-10

5.92825E-10

0.00150.001548.87668015

3.06895E-05

2.73028E-29

1.588E+12

5.58607E-31

3.51767E-43

1.70465E-10

9.26288E-10

1.60167E-19

0.002

0.002

48.8766802

4.09193E-05

4.85383E-29

2.82311E+12

9.93078E-31

3.51767E-43

3.03049E-10

1.64673E-09

1.60167E-19

0.003

0.003

48.8766803

6.1379E-05

1.09211E-28

6.35199E+122.23442E-30

3.51767E-43

6.81859E-10

3.70514E-09

1.60167E-19

1.60167E-19
1.60167E-19

1.60167E-19

1.60167E-19

0.004

0.004

48.8766804

8.18386E-05

1.94152E-28

1.12924E+13

3.97229E-30

3.51767E-43

1.21219E-09

0.005

0.005

48.8766805

0.000102298

3.03361E-28

1.76443E+13

6.20667E-30

3.51767E-43

1.89404E-09

1.0292E-08

1.60167E-19

0.01

0.01

48.876681

0.000204597

1.2134E-27

7.05744E+13

2.48258E-29

3.51767E-43

7.57585E-09

4.11664E-08

1.60167E-19

0.05
π/32

π/16

π/4

1.60167E-19

0.05

48.8767059

0.001022982

3.02986E-26

1.76224E+15

6.19898E-28

3.51767E-43

1.89169E-07

1.02792E-06

1.60167E-19

0.09817477

48.876779

0.002008619

1.16393E-25

6.76972E+15

2.38136E-27

3.51767E-43

7.26701E-07

3.94881E-06

1.60167E-19

0.1248.876828

0.002455154

1.73481E-25

1.00901E+16

3.54935E-27

3.51767E-43

1.08313E-06

5.88558E-06

1.60167E-19

0.15

48.8769105

0.003068939

2.69962E-25

1.57016E+16

5.52329E-27

3.51767E-43

1.6855E-06

9.1588E-06

1.60167E-19

0.17

48.8769763

0.003478127

3.45633E-25

2.01028E+16

7.07148E-27

3.51767E-43

2.15795E-06

1.1726E-05

1.60167E-19

0.196349541

π/8

6.58689E-09#DIV/0!

0.004017222

4.58834E-25

2.66868E+16

9.38751E-27

3.51767E-43

2.86471E-06

1.55665E-05

1.60168E-19

0.25

48.877319

0.005114869

7.34827E-25

4.27388E+16

1.50341E-26

3.51767E-43

4.58781E-06

2.49297E-05

1.60169E-19

0.3

48.877601

48.877075

0.006137819

1.04332E-24

6.06809E+16

2.13455E-26

3.51767E-43

6.51383E-06

3.53954E-05

1.6017E-19

0.3548.877933

0.007160757

1.39633E-24

8.12121E+16

2.85677E-26

3.51767E-43

8.71776E-06

4.73714E-05

1.60171E-19

0.392699082

48.878258

0.008034315

1.72881E-24

1.00549E+17

1.07935E-05

5.86504E-05

0.47

48.87894

0.009615741

2.38977E-24

1.38989E+17

4.88916E-26

3.51767E-43

1.49198E-05

8.10727E-05

1.60174E-19

0.55

48.879775

0.011252335

3.12918E-24

1.8199E+17

6.40179E-26

3.53697E-26

3.51767E-43

3.51767E-43

1.95358E-05

0.000106155

1.60176E-19

1.60172E-19

0.63

48.88074

0.012888869

3.89132E-24

2.2631E+17

7.96085E-26

3.51767E-43

2.42934E-05

0.000132008

1.6018E-19

0.71

48.881837

0.014525333

4.63845E-24

2.69756E+17

9.48911E-26

3.51767E-43

2.89571E-05

0.00015735

1.60183E-19

0.785398163

48.88299

0.016067592

5.29218E-24

3.07767E+17

1.08262E-25

3.51767E-43

3.30374E-05

0.000179522

1.60187E-19

0.81

48.883391

0.016570804

5.4887E-24

3.19193E+17

1.12282E-25

3.51767E-43

3.42639E-05

0.000186187

1.60189E-19

0.84

48.883898

0.017184418

5.71409E-24

3.32297E+17

1.16891E-25

3.51767E-43

3.56707E-05

0.00019383

1.6019E-19

0.87

48.884422

0.01779802

5.92159E-24

3.4436E+17

1.21135E-25

3.51767E-43

3.69655E-05

0.000200867

1.60193E-19

0.948.884965

0.018411609

6.10879E-24

3.55242E+17

1.24963E-25

3.51767E-43

3.81336E-05

0.000207214

1.60194E-19

0.93

48.885527

0.019025183

6.27327E-24

3.64803E+17

1.28326E-25

3.51767E-43

3.916E-05

0.000212791

1.60196E-19

0.935

48.885622

0.019127444

6.2983E-24

3.66258E+17

1.28838E-25

3.51767E-43

3.93161E-05

0.00021364

1.60197E-19

0.94

48.885718

0.019229705

6.32262E-24

3.67672E+17

1.29335E-25

3.51767E-43

3.94679E-05

0.000214464

1.60197E-19

0.945

48.8858145

0.019331965

6.34622E-24

3.69043E+17

1.29817E-25

3.51767E-43

3.96151E-05

0.000215265

1.60197E-19

0.95

48.885911

0.019434225

6.3691E-24

3.70372E+17

1.30285E-25

3.51767E-43

3.97577E-05

0.00021604

1.60198E-19

0.955

48.8860085

0.019536485

6.39122E-24

3.71658E+17

1.30737E-25

3.51767E-43

3.98958E-05

0.00021679

1.60198E-19

0.955148.8860108

0.01953853

6.39165E-24

3.71683E+17

1.30746E-25

3.51767E-43

3.98986E-05

0.000216805

1.60198E-19

0.955248.8860128

0.019540575

6.39209E-24

3.71709E+17

1.30755E-25

3.51767E-43

3.99013E-05

0.000216819

1.60198E-19

Θe0.955316618

48.886015

0.01954296

6.39259E-24

3.71738E+17

1.30765E-25

3.51767E-43

3.99044E-05

0.000216837

1.60198E-19

Θe×1.00000000000001

0.955316618

48.886015

0.01954296

6.39259E-24

3.71738E+17

1.30765E-25

3.51767E-43

3.99044E-05

0.000216837

1.60198E-19

0.96

48.886107

0.019638743

6.41258E-24

3.729E+17

1.31174E-25

3.51767E-43

4.00292E-05

0.000217514

1.60198E-19

0.97

48.886305

0.01984326

6.45301E-24

3.7525E+17

1.32E-25

3.51767E-43

4.02815E-05

0.000218885

1.60198E-19

0.98

48.886504

0.020047775

6.49028E-24

3.77415E+17

1.32762E-25

3.51767E-43

4.05139E-05

0.000220148

1.60199E-19

0.99

48.886706

0.020252289

6.5243E-24

3.79392E+17

1.33458E-25

3.51767E-43

4.07262E-05

0.000221301

1.60199E-19

1

48.886909

0.020456801

6.55499E-24

3.81175E+17

1.34085E-25

3.51767E-43

4.09175E-05

0.000222341

1.602E-19

1.047197551

48.887897

0.021422023

6.65202E-24

3.86809E+17

1.36067E-25

3.51767E-43

4.15223E-05

0.000225628

1.60204E-19

1.07

48.888391

0.021888334

6.66873E-24

3.87777E+17

1.36407E-25

3.51767E-43

4.16262E-05

0.000226192

1.60205E-19

1.1

1.60207E-19

1
π/3

B

48.889057

0.022501821

6.65841E-24

3.87172E+17

1.36194E-25

3.51767E-43

4.15613E-05

0.000225839

1.12

48.88951

0.022910804

6.63007E-24

3.8552E+17

1.35613E-25

3.51767E-43

4.13838E-05

0.000224876

1.6021E-19

1.15

48.890207

0.023524263

6.5536E-24

3.81068E+17

1.34047E-25

3.51767E-43

4.0906E-05

0.000222279

1.60211E-19

1.170019129

48.890682

0.023933617

6.4789E-24

3.76721E+17

1.32518E-25

3.51767E-43

4.04393E-05

0.000219743

1.60213E-19

1.23

48.892155

0.025160065

6.13414E-24

3.56665E+17

1.25463E-25

3.51767E-43

3.82865E-05

0.000208044

1.60217E-19

1.23788593

48.892354

0.025321305

6.07467E-24

3.53206E+17

1.24246E-25

3.51767E-43

3.79152E-05

0.000206026

1.60217E-19

1.27

48.893177

0.025977916

5.79683E-24

3.37044E+17

1.18561E-25

3.51767E-43

3.61802E-05

0.000196599

1.60221E-19

1.351

48.895348

0.027633957

4.82713E-24

2.80651E+17

9.87236E-26

3.51767E-43

3.01266E-05

0.000163705

1.37

48.895877

0.02802239

4.54077E-24

2.63999E+17

9.28662E-26

3.51767E-43

2.83392E-05

0.000153992

1.60229E-19

1.47

48.898781

0.030066629

2.63738E-24

1.53328E+17

5.39355E-26

3.51767E-43

1.64591E-05

8.94366E-05

1.60239E-19

1.48

48.899082

0.03027104

2.40892E-24

1.40044E+17

4.9263E-26

3.51767E-43

1.50331E-05

8.16885E-05

1.60241E-19

1.60228E-19

1.49

48.8993855

0.030475448

2.17328E-24

1.26345E+17

4.44439E-26

3.51767E-43

1.35625E-05

7.36974E-05

1.60242E-19

1.5

48.8996913

0.030679853

1.93042E-24

1.12225E+17

3.94772E-26

3.51767E-43

1.20469E-05

6.54615E-05

1.60243E-19

1.51

48.899999

0.030884256

1.68028E-24

9.76828E+16

3.43616E-26

3.51767E-43

1.04858E-05

5.69788E-05

1.60244E-19

1.52

48.900309

0.031088656

1.42282E-24

8.27145E+16

2.90963E-26

3.51767E-43

8.87903E-06

4.82478E-05

1.60245E-19

1.53

48.9006208

0.031293053

1.15797E-24

6.73173E+16

2.368E-26

3.51767E-43

7.22621E-06

3.92665E-05

1.60246E-19

1.54

48.9009345

0.031497448

8.85691E-25

5.14884E+16

1.81119E-26

3.51767E-43

5.52704E-06

3.00334E-05

1.60247E-19

1.55

48.9012505

0.031701841

6.05936E-25

3.5225E+16

1.2391E-26

3.51767E-43

3.78124E-06

2.05469E-05

1.60248E-19

1.56

48.901569

0.03190623

3.18656E-25

1.85244E+16

6.51627E-27

3.51767E-43

1.98851E-06

1.08053E-05

1.60248E-19

π/2×0.999999999890292

1.570796327

48.901915

0.032126893

5.15704E-33

299791839.4

1.05457E-34

3.51767E-43

3.21814E-14

1.7487E-13

1.60249E-19

π/2×0.999999999996476

1.570796327

48.9019152

0.032126892

1.65657E-34

9630038.373

3.38753E-36

3.51767E-43

1.03375E-15

5.61724E-15

1.60249E-19

π/2×0.999999999999999
π/2

1.570796327
1.570796327

48.9019152
48.9019152

0.032126892
0.032126892

4.17019E-38
1.83316E-39

2424.239306
106.5661875

8.52766E-40
3.74864E-41

3.51767E-43
3.51767E-43

2.60232E-19
1.14394E-20

1.41407E-18
6.21605E-20

1.60249E-19
1.60249E-19

1/1 ページ

file://C:\Documents%20and%20Settings\新美\デスクトップ\F.I.T\yoko.host\gaps-t.web\gaps-t.graph\graph.2.htm

2005/12/13

case ④(wτ=48.87668)

ωτ= wτsinθ

value of [ωτ]0[c]

ω2exp(+ρ)cosδ/(σ 2+ω2)=[ ]sin2θexp(wτcosθ)cos(wτsinθ)θ=asin(ωτ/wτ)ω2exp(-ρ)cosδ/(σ 2+ω2)=

ratio/c=3.51767E-43

sin2θexp(-wτcosθ)cos(wτsinθ)

0

0

0

0

π/2×0.00000000000553261063

8.6906E-12

1.77807E-13

5.33051E-05

1.8751E-47

3.51767E-43

π/2×0.00000002927 57

4.59862E-08

9.40861E-10

1492.53097

5.25023E-40

3.51767E-43

π/2×0.00001312066853

2.06099E-05

4.21671E-07

299792458

1.05457E-34

3.51767E-43

0.001

0.001

2.04597E-05

7.05779E+112.4827E-31

3.51767E-43

0.001001

0.001001

2.04801E-05

7.07191E+11

2.48767E-31

3.51767E-43

0.001005

0.001005

2.0562E-05

7.12855E+11

2.50759E-31

3.51767E-43

0.00101

0.00101

2.06643E-05

7.19965E+11

2.5326E-31

3.51767E-43

0.001020.001022.08688E-05

7.34293E+11

2.583E-31

3.51767E-43

0.00105

0.00105

2.14826E-05

7.78121E+11

2.73717E-31

3.51767E-43

0.00110.00112.25056E-05

8.53993E+11

3.00406E-31

3.51767E-43

0.00120.00122.45516E-05

1.01632E+12

3.57508E-31

3.51767E-43

0.00150.00153.06895E-05

1.588E+12

5.58607E-31

3.51767E-43

0.002

0.002

4.09193E-05

2.82311E+12

9.93078E-31

3.51767E-43

0.003

0.003

6.1379E-05

6.35199E+122.23442E-30

3.51767E-43

0.004

0.004

8.18386E-05

1.12924E+13

3.97229E-30

3.51767E-43

0.005

0.005

0.000102298

1.76443E+13

6.20667E-30

3.51767E-43

0.01

0.01

0.000204597

7.05743E+13

2.48258E-29

3.51768E-43

0.05

0.05

0.001022983

1.7622E+15

6.19915E-28

3.51785E-43

0.09817477

0.002008623

6.76908E+15

2.38161E-27

3.51836E-43

0.12

0.002455161

1.00887E+16

3.5499E-27

3.51871E-43

0.15

0.003068953

1.56981E+16

5.52462E-27

3.51929E-43

0.17

0.003478148

2.00971E+16

7.07366E-27

3.51975E-43

0.196349541

0.004017255

2.66767E+16

9.39138E-27

3.52045E-43

0.25

0.005114936

4.27126E+16

1.50441E-26

3.52217E-43

0.3

0.006137935

6.06273E+16

2.1366E-26

3.52415E-43

0.35

0.00716094

8.11146E+16

2.8605E-26

3.5265E-43

0.392699082

0.008034574

1.00397E+17

3.54278E-26

3.52879E-43

0.47

0.009616186

1.38688E+17

4.90068E-26

3.53361E-43

0.55

0.011253048

1.8145E+17

6.42245E-26

3.53951E-43

0.63

0.012889939

2.25431E+17

7.99456E-26

3.54635E-43

0.71

0.014526866

2.68425E+17

9.54019E-26

3.55414E-43

0.785398163

0.016069667

3.0591E+17

1.08976E-25

3.56235E-43

0.81

0.016573079

3.17145E+17

1.13069E-25

3.56521E-43

0.84

0.017186956

3.30004E+17

1.17773E-25

3.56882E-43

0.87

0.01780084

3.41812E+17

1.22115E-25

3.57257E-43

0.90.01841473

3.5243E+17

1.26045E-25

3.57646E-43

0.93

0.019028627

3.6172E+17

1.29513E-25

3.58048E-43

0.935

0.019130944

3.6313E+17

1.30043E-25

3.58116E-43

0.94

0.019233261

3.64498E+17

1.30558E-25

3.58185E-43

0.945

0.019335579

3.65824E+17

1.31058E-25

3.58254E-43

0.95

0.019437896

3.67107E+17

1.31543E-25

3.58323E-43

0.955

0.019540214

3.68347E+17

1.32013E-25

3.58393E-43

0.95510.01954226

3.68371E+17

1.32022E-25

3.58395E-43

0.95520.019544306

3.68396E+17

1.32032E-25

3.58396E-43

Θe0.955316618

0.019546693

3.68424E+17

1.32042E-25

3.58398E-43

Θe×1.00000000000001

0.955316618

0.019546693

3.68424E+17

1.32042E-25

3.58398E-43

0.96

0.019642532

3.69543E+17

1.32468E-25

3.58463E-43

0.97

0.019847168

3.71801E+17

1.3333E-25

3.58605E-43

0.98

0.020051805

3.73875E+17

1.34127E-25

3.58748E-43

0.99

0.020256443

3.75761E+17

1.34858E-25

3.58893E-43

10.020461082

3.77453E+17

1.3552E-25

3.59039E-43

1.047197551

0.02142694

3.82669E+17

1.37665E-25

3.5975E-43

1.07

0.02189358

3.83445E+17

1.38081E-25

3.60105E-43

π/32

π/16

π/8

π/4

1
π/3

#DIV/0!

1.1

0.022507521

3.82602E+17

1.37961E-25

3.60585E-43

1.12

0.022916819

3.80804E+17

1.37437E-25

3.60913E-43

1.15

0.023530774

3.76155E+17

1.35949E-25

3.61416E-43

1.170019129

0.023940474

3.71694E+17

1.34464E-25

3.6176E-43

1.27

0.025986686

3.31752E+17

1.20615E-25

3.63571E-43

1.351

0.027644515

2.75669E+17

1.00661E-25

3.65154E-43

1.37

0.028033399

2.59181E+17

9.47412E-26

3.65541E-43

1.47

0.030080229

1.5011E+17

5.51913E-26

3.67672E-43

1.48

0.030284918

1.37066E+17

5.04258E-26

3.67894E-43

1.49

0.030489609

1.23622E+17

4.55073E-26

3.68118E-43

1.50.030694302

1.09774E+17

4.04346E-26

3.68343E-43

1.51

0.030898995

9.55213E+16

3.52063E-26

3.6857E-43

1.52

0.03110369

8.08602E+16

2.98211E-26

3.68799E-43

1.53

0.031308386

6.57885E+16

2.42779E-26

3.69029E-43

1.54

0.031513084

5.03039E+16

1.85753E-26

3.69261E-43

1.55

0.031717783

3.44042E+16

1.27122E-26

3.69495E-43

1.56

0.031922483

1.80872E+16

6.68737E-27

3.6973E-43

π/2×0.999999999890292

1.570796327

0.032143485

292618608.9

1.08265E-34

3.69986E-43

π/2×0.999999999996476

1.570796327

0.032143485

9399639.294

3.47773E-36

3.69986E-43

π/2

1.570796327

0.032143485

104.0165869

3.84847E-41

3.69986E-43

B

Case A(wτ=48.87668)

ωτθωτ= wτsinθ
0
π/2×0.00000000000553261063
π/2×0.00000002927 57
π/2×0.00001312066853
0.001
0.001001
0.001005
0.00101
0.001020.00105
0.00110.00120.0015
0.002
0.003
0.004
0.005
0.01
0.05
π/32

π/16

π/8

π/4

Θe
Θe×1.00000000000001

1
π/3

B

π/2×0.999999999890292
π/2×0.999999999996476
π/2×0.999999999999999
π/2[M τsinθ][ v ] cω2exp(+ρ)cosδ/(σ 2+ω2)=ωτsinθexp(-ρ)cosδ=value of [ωτ]θ=asin(ωτ/wτ)wτsin2θexp(-wτcosθ)cos(wτsinθ)08.6906E-12
4.59862E-08
2.06099E-05
0.001
0.001001
0.001005
0.00101
0.001020.00105
0.00110.00120.0015
0.002
0.003
0.004
0.005
0.01
0.05
0.09817477
0.12
0.15
0.17
0.196349541
0.25
0.3
0.35
0.392699082
0.47
0.55
0.63
0.71
0.785398163
0.81
0.84
0.87
0.9
0.93
0.935
0.94
0.945
0.95
0.955
0.95510.95520.955316618
0.955316618
0.96
0.97
0.98
0.99
1
1.047197551
1.07
1.1
1.12
1.15
1.170019129
1.23
1.23788593
1.27
1.351
1.37
1.47
1.48
1.49
1.5
1.51
1.52
1.53
1.54
1.55
1.56
1.570796327
1.570796327
1.570796327
1.570796327

01.77807E-13
9.40861E-10
4.21671E-07
2.04597E-05
2.04801E-05
2.0562E-05
2.06643E-05
2.08688E-05
2.14826E-05
2.25056E-05
2.45516E-05
3.06895E-05
4.09193E-05
6.1379E-05
8.18386E-05
0.000102298
0.000204597
0.001022983
0.002008623
0.002455161
0.003068953
0.003478148
0.004017255
0.005114936
0.006137935
0.00716094
0.008034574
0.009616186
0.011253048
0.012889939
0.014526866
0.016069667
0.016573079
0.017186956
0.01780084
0.01841473
0.019028627
0.019130944
0.019233261
0.019335579
0.019437896
0.019540214
0.01954226
0.019544306
0.019546693
0.019546693
0.019642532
0.019847168
0.020051805
0.020256443
0.020461082
0.02142694
0.02189358
0.022507521
0.022916819
0.023530774
0.023940474
0.025168032
0.025329427
0.025986686
0.027644515
0.028033399
0.030080229
0.030284918
0.030489609
0.030694302
0.030898995
0.03110369
0.031308386
0.031513084
0.031717783
0.031922483
0.032143485
0.032143485
0.032143485
0.032143485

09.16486E-46
2.56614E-38
5.15439E-33
1.21346E-29
1.21589E-29
1.22563E-29
1.23785E-29
1.26248E-29
1.33784E-29
1.46829E-29
1.74738E-29
2.73028E-29
4.85384E-29
1.09211E-28
1.94152E-28
3.03362E-28
1.2134E-27
3.02994E-26
1.16405E-25
1.73507E-25
2.70025E-25
3.45737E-25
4.59019E-25
7.35306E-25
1.0443E-24
1.39812E-24
1.73159E-24
2.39529E-24
3.13908E-24
3.90748E-24
4.66293E-24
5.32637E-24
5.52643E-24
5.75634E-24
5.96857E-24
6.16067E-24
6.33017E-24
6.35605E-24
6.38122E-24
6.40567E-24
6.42939E-24
6.45236E-24
6.45281E-24
6.45326E-24
6.45379E-24
6.45379E-24
6.47458E-24
6.51671E-24
6.55568E-24
6.59141E-24
6.62378E-24
6.72862E-24
6.74892E-24
6.74306E-24
6.71747E-24
6.64472E-24
6.57216E-24
6.23181E-24
6.17265E-24
5.89527E-24
4.92E-24
4.63064E-24
2.69757E-24
2.46464E-24
2.22425E-24
1.97631E-24
1.72077E-24
1.45756E-24
1.18662E-24
9.07897E-25
6.21328E-25
3.26857E-25
5.29162E-33
1.6998E-34
4.96085E-38
1.881E-39

csin2θexp(wτcosθ)cos(wτsinθ)05.33051E-05
1492.53097
299792458
7.05779E+11
7.07191E+117.12855E+11
7.19965E+11
7.34293E+11
7.78121E+11
8.53993E+11
1.01632E+12
1.588E+122.82311E+12
6.35199E+121.12924E+13
1.76443E+13
7.05743E+13
1.7622E+15
6.76908E+15
1.00887E+16
1.56981E+16
2.00971E+16
2.66767E+16
4.27126E+16
6.06273E+16
8.11146E+16
1.00397E+17
1.38688E+17
1.8145E+172.25431E+17
2.68425E+17
3.0591E+17
3.17145E+17
3.30004E+17
3.41812E+17
3.5243E+17
3.6172E+17
3.6313E+17
3.64498E+17
3.65824E+17
3.67107E+17
3.68347E+17
3.68371E+17
3.68396E+17
3.68424E+17
3.68424E+17
3.69543E+17
3.71801E+17
3.73875E+17
3.75761E+17
3.77453E+17
3.82669E+17
3.83445E+17
3.82602E+17
3.80804E+17
3.76155E+17
3.71694E+17
3.51408E+17
3.47934E+17
3.31752E+17
2.75669E+17
2.59181E+17
1.5011E+17
1.37066E+17
1.23622E+17
1.09774E+17
9.55213E+16
8.08602E+16
6.57885E+16
5.03039E+16
3.44042E+16
1.80872E+16292618608.9
9399639.294
2743.276392
104.0165869[]

ω2exp(-ρ)cosδ/(σ 2+ω2)=

ratio/c=3.51767E-43

sin2θexp(-wτcosθ)cos(wτsinθ)01.8751E-47
5.25023E-40
1.05457E-34
2.4827E-31
2.48767E-31
2.50759E-31
2.5326E-31
2.583E-31
2.73717E-31
3.00406E-31
3.57508E-31
5.58607E-31
9.93078E-31
2.23442E-30
3.97229E-30
6.20667E-30
2.48258E-29
6.19915E-28
2.38161E-27
3.5499E-27
5.52462E-27
7.07366E-27
9.39138E-27
1.50441E-26
2.1366E-26
2.8605E-26
3.54278E-26
4.90068E-26
6.42245E-26
7.99456E-26
9.54019E-26
1.08976E-25
1.13069E-25
1.17773E-25
1.22115E-25
1.26045E-25
1.29513E-25
1.30043E-25
1.30558E-25
1.31058E-25
1.31543E-25
1.32013E-25
1.32022E-25
1.32032E-25
1.32042E-25
1.32042E-25
1.32468E-25
1.3333E-25
1.34127E-25
1.34858E-25
1.3552E-25
1.37665E-25
1.38081E-25
1.37961E-25
1.37437E-25
1.35949E-25
1.34464E-25
1.27501E-25
1.2629E-25
1.20615E-25
1.00661E-25
9.47412E-26
5.51913E-26
5.04258E-26
4.55073E-26
4.04346E-26
3.52063E-26
2.98211E-26
2.42779E-26
1.85753E-26
1.27122E-26
6.68737E-27
1.08265E-34
3.47773E-36
1.01497E-39
3.84847E-41[QR] Qω2exp(-iρ)cosδ/(σ 2+ω2)=
Qsin2θcos(wτcosθ)cos(wτsinθ) -#DIV/0!
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51767E-43
3.51768E-43
3.51785E-43
3.51836E-43
3.51871E-43
3.51929E-43
3.51975E-43
3.52045E-43
3.52217E-43
3.52415E-43
3.5265E-43
3.52879E-43
3.53361E-43
3.53951E-43
3.54635E-43
3.55414E-43
3.56235E-43
3.56521E-43
3.56882E-43
3.57257E-43
3.57646E-43
3.58048E-43
3.58116E-43
3.58185E-43
3.58254E-43
3.58323E-43
3.58393E-43
3.58395E-43
3.58396E-43
3.58398E-43
3.58398E-43
3.58463E-43
3.58605E-43
3.58748E-43
3.58893E-43
3.59039E-43
3.5975E-43
3.60105E-43
3.60585E-43
3.60913E-43
3.61416E-43
3.6176E-43
3.62827E-43
3.62972E-43
3.63571E-43
3.65154E-43
3.65541E-43
3.67672E-43
3.67894E-43
3.68118E-43
3.68343E-43
3.6857E-43
3.68799E-43
3.69029E-43
3.69261E-43
3.69495E-43
3.6973E-43
3.69986E-43
3.69986E-43
3.69986E-43
3.69986E-43

05.72207E-27
1.60217E-19
3.21814E-14
7.57623E-11
7.59139E-11
7.65218E-11
7.72851E-11
7.88231E-11
8.35279E-11
9.16723E-11
1.09098E-10
1.70465E-10
3.03049E-10
6.81857E-10
1.21219E-09
1.89403E-09
7.57581E-09
1.89143E-07
7.26313E-07
1.08226E-06
1.6834E-06
2.1545E-06
2.85861E-06
4.572E-06
6.48147E-06
8.65884E-06
1.07016E-05
1.47379E-05
1.92096E-05
2.37611E-05
2.81512E-05
3.19121E-05
3.30225E-05
3.42806E-05
3.54202E-05
3.64276E-05
3.72891E-05
3.74175E-05
3.75415E-05
3.76609E-05
3.77757E-05
3.78858E-05
3.7888E-05
3.78901E-05
3.78926E-05
3.78926E-05
3.79912E-05
3.81876E-05
3.83642E-05
3.85208E-05
3.86568E-05
3.90062E-05
3.89925E-05
3.87819E-05
3.85147E-05
3.79157E-05
3.73792E-05
3.50838E-05
3.47026E-05
3.29533E-05
2.7085E-05
2.53968E-05
1.44908E-05
1.32108E-05
1.18961E-05
1.05467E-05
9.16248E-06
7.74354E-06
6.28985E-06
4.80144E-06
3.27834E-06
1.7206E-06
2.77851E-14
8.92526E-16
2.60483E-19
9.87671E-21

electron[QI]
i Qsin2θsin(wτcosθ)cos(wτsinθ)03.10931E-26
8.706E-19
1.7487E-13
4.11684E-10
4.12508E-10
4.15811E-10
4.19959E-10
4.28316E-10
4.53882E-10
4.98138E-10
5.92825E-10
9.26289E-10
1.64673E-09
3.70514E-09
6.5869E-09
1.0292E-08
4.11664E-08
1.02793E-06
3.9489E-06
5.88578E-06
9.15927E-06
1.17268E-05
1.55679E-05
2.49333E-05
3.54027E-05
4.73847E-05
5.86712E-05
8.11137E-05
0.000106229
0.000132127
0.00015753
0.000179773
0.000186464
0.00019414
0.000201211
0.000207594
0.000213206
0.000214061
0.000214892
0.000215698
0.000216479
0.000217236
0.00021725
0.000217265
0.000217283
0.000217283
0.000217966
0.000219349
0.000220624
0.000221789
0.000222841
0.000226183
0.000226773
0.000226451
0.000225507
0.000222935
0.000220414
0.000208744
0.000206728
0.000197303
0.000164364
0.000154629
8.98598E-05
8.20801E-05
7.40552E-05
6.57834E-05
5.72626E-05
4.8491E-05
3.9467E-05
3.01886E-05
2.06544E-05
1.08626E-05
1.75807E-13
5.64737E-15
1.64818E-18
6.24939E-20

q = M τsinθ/Q R#DIV/0!
1.60167E-19
1.60167E-19
1.60167E-19
1.60167E-19
1.60167E-19
1.60167E-19
1.60167E-19
1.60167E-19
1.60167E-19
1.60167E-19
1.60167E-19
1.60167E-19
1.60167E-19
1.60167E-19
1.60167E-19
1.60167E-19
1.60168E-19
1.60193E-19
1.60269E-19
1.60319E-19
1.60404E-19
1.60472E-19
1.60574E-19
1.60828E-19
1.61121E-19
1.61467E-19
1.61807E-19
1.62525E-19
1.63412E-19
1.64448E-19
1.65639E-19
1.66908E-19
1.67353E-19
1.67918E-19
1.68507E-19
1.69121E-19
1.69759E-19
1.69868E-19
1.69978E-19
1.70088E-19
1.70199E-19
1.70311E-19
1.70313E-19
1.70315E-19
1.70318E-19
1.70318E-19
1.70423E-19
1.7065E-19
1.7088E-19
1.71113E-19
1.71349E-19
1.72501E-19
1.73082E-19
1.73871E-19
1.74413E-19
1.7525E-19
1.75824E-19
1.77627E-19
1.77873E-19
1.78898E-19
1.8165E-19
1.82332E-19
1.86158E-19
1.86563E-19
1.86973E-19
1.87387E-19
1.87806E-19
1.88229E-19
1.88656E-19
1.89088E-19
1.89525E-19
1.89966E-19
1.90448E-19
1.90448E-19
1.90448E-19
1.90448E-19

Case B(wτ=48.886015)ωτθωτ= wτsinθ

value of [ωτ]0[M τsinθ]0[ ]csin2θexp(wτcosθ)cos(wτsinθ)ω2exp(-ρ)cosδ/(σ 2+ω2)=

ratio/c=3.51767E-43

sin2θexp(-wτcosθ)cos(wτsinθ)[QR] Qω2exp(-iρ)cosδ/(σ 2+ω2)=

0#DIV/0!

electron[QI]

Qsin2θcos(wτcosθ)cos(wτsinθ) -i Qsin2θsin(wτcosθ)cos(wτsinθ)q = M τsinθ/Q R

0

0

0

0

π/2×0.00000000000553261063

8.6906E-12

1.77773E-13

9.07797E-46

5.37845E-05

1.85697E-47

3.4526E-43

6.00978E-27

3.10265E-26

1.51053E-19

π/2×0.00000002927 57

4.59862E-08

9.40681E-10

2.54181E-38

1505.953679

5.19946E-40

3.4526E-43

1.68272E-19

8.68734E-19

1.51053E-19

π/2×0.00001312066853

0[ v ] cω2exp(+ρ)cosδ/(σ 2+ω2)=ωτsinθexp(-ρ)cosδ=wτsin2θexp(-wτcosθ)cos(wτsinθ)θ=asin(ωτ/wτ)#DIV/0!

2.06099E-05

4.21591E-07

5.10553E-33

302488567.5

1.04437E-34

3.4526E-43

3.37995E-14

1.74496E-13

1.51053E-19

0.001

0.001

2.04557E-05

1.20196E-29

7.12126E+11

2.45869E-31

3.45261E-43

7.95716E-11

4.10802E-10

1.51053E-19

0.001001

0.001001

2.04762E-05

1.20436E-29

7.13551E+11

2.46361E-31

3.45261E-43

7.97308E-11

4.11624E-10

1.51053E-19

0.001005

0.001005

2.0558E-05

1.21401E-29

7.19265E+11

2.48334E-31

3.45261E-43

8.03693E-11

4.1492E-10

1.51053E-19

0.00101

0.00101

2.06603E-05

1.22612E-29

7.2644E+11

2.50811E-31

3.45261E-43

8.1171E-11

4.19059E-10

1.51053E-19

0.001020.001022.08649E-05

1.25052E-29

7.40896E+11

2.55802E-31

3.45261E-43

8.27863E-11

4.27398E-10

1.51053E-19

0.00105

0.00105

2.14785E-05

1.32516E-29

7.85119E+112.71071E-31

3.45261E-43

8.77277E-11

4.52909E-10

1.51053E-19

0.00110.00112.25013E-05

1.45437E-29

8.61673E+11

2.97502E-31

3.45261E-43

9.62816E-11

4.9707E-10

1.51053E-19

0.00120.00122.45469E-05

1.73082E-29

1.02546E+12

3.54051E-31

3.45261E-43

1.14583E-10

5.91555E-10

1.51053E-19

0.00150.00153.06836E-05

2.7044E-29

1.60228E+12

5.53205E-31

3.45261E-43

1.79036E-10

9.24304E-10

1.51053E-19

0.002

0.002

4.09115E-05

4.80782E-29

2.8485E+12

9.83475E-31

3.45261E-43

3.18286E-10

1.64321E-09

1.51053E-19

0.003

0.003

6.13672E-05

1.08176E-28

6.40911E+12

2.21281E-30

3.45261E-43

7.16141E-10

3.6972E-09

1.51053E-19

0.004

0.004

8.1823E-05

1.92312E-28

1.13939E+13

3.93388E-30

3.45261E-43

1.27313E-09

6.57278E-09

0.005

0.005

0.000102279

3.00485E-28

1.78029E+13

6.14666E-30

3.45261E-43

1.98926E-09

1.02699E-08

1.51054E-19

0.01

0.01

0.000204557

1.2019E-27

7.1209E+13

2.45857E-29

3.45261E-43

7.95672E-09

4.10782E-08

1.51054E-19

0.05

0.05

0.001022788

3.00121E-26

1.77805E+15

6.13921E-28

3.45278E-43

1.98654E-07

1.02573E-06

1.51077E-19

0.09817477

0.00200824

1.15302E-25

6.82996E+15

2.35858E-27

3.45329E-43

7.62853E-07

3.94044E-06

1.51145E-19

0.12

0.002454692

1.71862E-25

1.01794E+16

3.51557E-27

3.45362E-43

1.13673E-06

5.87318E-06

1.51191E-19

0.15

0.003068367

2.67465E-25

1.58393E+16

5.4712E-27

3.45419E-43

1.76815E-06

9.13967E-06

1.51268E-19

π/32

π/16

π/8

0.17

0.003477484

3.42459E-25

2.02778E+16

7.00526E-27

3.45465E-43

2.26301E-06

1.17017E-05

1.51329E-19

0.196349541

0.004016488

4.54667E-25

2.69166E+16

9.30056E-27

3.45533E-43

3.00267E-06

1.55346E-05

1.51421E-19

0.25

0.005113959

7.28335E-25

4.30967E+16

1.48986E-26

3.45702E-43

4.80272E-06

2.488E-05

1.5165E-19

0.3

0.006136763

1.0344E-24

6.11725E+16

2.11594E-26

3.45897E-43

6.80908E-06

3.53272E-05

1.51915E-19

0.35

0.007159573

1.38486E-24

8.18441E+16

2.83284E-26

3.46127E-43

9.09732E-06

4.72837E-05

1.52228E-19

0.392699082

π/41.51054E-19

0.00803304

1.71518E-24

1.013E+17

3.50852E-26

3.46351E-43

1.12445E-05

5.85464E-05

1.52534E-19

0.47

0.00961435

2.37258E-24

1.39935E+17

4.85328E-26

3.46824E-43

1.54886E-05

8.09416E-05

1.53182E-19

0.55

0.011250899

3.10932E-24

1.83082E+17

6.36034E-26

3.47404E-43

2.01927E-05

0.000106004

1.53982E-19

0.63

0.012887478

3.87043E-24

2.27458E+17

7.91725E-26

3.48075E-43

2.49841E-05

0.000131849

1.54916E-19

0.71

0.014524092

4.61872E-24

2.70839E+17

9.44793E-26

3.48839E-43

2.96093E-05

0.0001572

1.55989E-19

0.785398163

0.016066598

5.27587E-24

3.08661E+17

1.07922E-25

3.49645E-43

3.35762E-05

0.000179399

1.57131E-19

0.81

0.016569914

5.47402E-24

3.19997E+17

1.11975E-25

3.49926E-43

3.47487E-05

0.000186076

1.57532E-19

0.840.017183674

5.70176E-24

3.32973E+17

1.16634E-25

3.5028E-43

3.60779E-05

0.000193738

0.87

0.01779744

5.91197E-24

3.44887E+17

1.20934E-25

3.50648E-43

3.7283E-05

0.000200795

1.5857E-19

0.90.018411213

6.10225E-24

3.556E+17

1.24826E-25

3.51029E-43

3.83496E-05

0.000207165

1.59122E-19

0.930.019024993

6.27014E-24

3.64974E+17

1.2826E-25

3.51424E-43

3.92631E-05

0.000212768

1.59696E-19

0.935

1.5804E-19

0.019127291

6.29578E-24

3.66396E+17

1.28785E-25

3.51491E-43

3.93994E-05

0.000213621

1.59794E-19

0.94

0.019229588

6.32071E-24

3.67776E+17

1.29295E-25

3.51558E-43

3.95311E-05

0.00021445

1.59892E-19

0.945

0.019331886

6.34493E-24

3.69114E+17

1.2979E-25

3.51626E-43

3.9658E-05

0.000215255

1.59991E-19

0.95

0.019434184

6.36842E-24

3.70409E+17

1.30271E-25

3.51694E-43

3.978E-05

0.000216035

1.60091E-19

0.955

0.019536482

6.39118E-24

3.7166E+17

1.30736E-25

3.51763E-43

3.98972E-05

0.00021679

1.60191E-19

0.95510.019538528

6.39162E-24

3.71685E+17

1.30745E-25

3.51764E-43

3.98995E-05

0.000216804

1.60193E-19

0.95520.019540574

6.39207E-24

3.7171E+17

1.30755E-25

3.51766E-43

3.99018E-05

0.000216819

1.60195E-19

Θe0.955316618

0.01954296

6.39259E-24

3.71738E+17

1.30765E-25

3.51767E-43

3.99044E-05

0.000216837

1.60198E-19

Θe×1.00000000000001

0.955316618

0.01954296

6.39259E-24

3.71738E+17

1.30765E-25

3.51767E-43

3.99044E-05

0.000216837

1.60198E-19

0.96

0.01963878

6.41319E-24

3.72867E+17

1.31187E-25

3.51832E-43

4.00093E-05

0.000217519

1.60292E-19

0.97

0.019843378

6.45492E-24

3.75145E+17

1.3204E-25

3.51971E-43

4.02185E-05

0.000218899

1.60496E-19

0.98

0.020047976

6.49352E-24

3.77238E+17

1.3283E-25

3.52111E-43

4.0407E-05

0.000220172

1.60703E-19

0.99

0.020252575

6.5289E-24

3.79141E+17

1.33554E-25

3.52253E-43

4.05744E-05

0.000221335

1.60912E-19

10.020457175

6.56097E-24

3.80848E+17

1.3421E-25

3.52397E-43

4.07201E-05

0.000222385

1.61123E-19

1.047197551

0.021422848

6.66481E-24

3.86112E+17

1.36334E-25

3.53094E-43

4.11006E-05

0.000225723

1.62158E-19

1.07

0.021889398

6.68492E-24

3.86894E+17

1.36745E-25

3.53443E-43

4.10925E-05

0.000226312

1.6268E-19

1.1

0.022503222

6.67911E-24

3.86044E+17

1.36626E-25

3.53914E-43

4.0879E-05

0.000225993

1.63387E-19

1.12

0.022912442

6.65377E-24

3.8423E+17

1.36108E-25

3.54236E-43

4.06032E-05

0.000225051

1.63873E-19

1
π/3

B

π/2×0.999999999890292

1.15

0.02352628

6.58171E-24

3.79539E+17

1.34634E-25

3.5473E-43

3.99805E-05

0.000222487

1.64623E-19

1.170019129

0.023935902

6.50984E-24

3.75038E+17

1.33164E-25

3.55067E-43

3.94206E-05

0.000219971

1.65138E-19

1.23

0.025163225

6.17271E-24

3.5457E+17

1.26267E-25

3.56114E-43

3.70173E-05

0.000208327

1.66752E-19

1.23788593

0.025324589

6.11411E-24

3.51064E+17

1.25069E-25

3.56256E-43

3.66175E-05

0.000206316

1.66972E-19
1.67889E-19

1.27

0.025981723

5.83936E-24

3.34736E+17

1.19449E-25

3.56844E-43

3.4781E-05

0.000196911

1.351

0.027639234

4.87334E-24

2.78149E+17

9.96877E-26

3.58397E-43

2.86078E-05

0.000164041

1.7035E-19

1.37

0.028028044

4.58672E-24

2.61513E+17

9.38247E-26

3.58777E-43

2.68294E-05

0.000154326

1.70959E-19

1.47

0.030074483

2.67198E-24

1.51461E+17

5.46574E-26

3.60868E-43

1.53235E-05

8.96863E-05

1.74372E-19

1.48

0.030279134

2.44127E-24

1.38299E+17

4.9938E-26

3.61086E-43

1.39714E-05

8.19218E-05

1.74733E-19

1.49

0.030483785

2.20315E-24

1.24734E+17

4.50671E-26

3.61305E-43

1.25824E-05

7.39127E-05

1.75098E-19
1.75467E-19

1.50.030688439

1.95756E-24

1.10762E+17

4.00434E-26

3.61527E-43

1.11563E-05

6.56569E-05

1.51

0.030893093

1.70444E-24

9.63808E+16

3.48657E-26

3.61749E-43

9.69317E-06

5.71527E-05

1.7584E-19

1.52

0.031097749

1.44373E-24

8.15877E+16

2.95326E-26

3.61974E-43

8.19295E-06

4.83981E-05

1.76216E-19

1.53

0.031302406

1.17537E-24

6.63804E+16

2.4043E-26

3.622E-43

6.65563E-06

3.93914E-05

1.76597E-19

1.54

0.031507064

8.99285E-25

5.07565E+16

1.83956E-26

3.62427E-43

5.08124E-06

3.0131E-05

1.76982E-19

1.55

0.031711724

6.15435E-25

3.47138E+16

1.25892E-26

3.62657E-43

3.46978E-06

2.0615E-05

1.7737E-19

1.56

0.031916385

3.23756E-25

1.82499E+16

6.62268E-27

3.62888E-43

1.82128E-06

1.08419E-05

1.77763E-19

1.570796327

0.032137345

5.24143E-33

295252006.8

1.07217E-34

3.63139E-43

2.94147E-14

1.75473E-13

1.78191E-19

π/2×0.999999999996476

1.570796327

0.032137345

1.68354E-34

9483457.519

3.44381E-36

3.63139E-43

9.44795E-16

5.63619E-15

1.78191E-19

π/2×0.999999999999999
π/2

1.570796327
1.570796327

0.032137345
0.032137345

4.9138E-38
8.6167E-39

2767.960723
485.382281

1.00515E-39
1.76261E-40

3.63139E-43
3.63139E-43

2.7576E-19
4.83565E-20

1.64505E-18
2.88471E-19

1.78191E-19
1.78191E-19

Case C(wτ=48.892354)ωτθωτ= wτsinθ

value of [ωτ]0

π/2×0.00000000000553261063[M τsinθ][ v ] cω2exp(+ρ)cosδ/(σ 2+ω2)=ωτsinθexp(-ρ)cosδ=wτsin2θexp(-wτcosθ)cos(wτsinθ)θ=asin(ωτ/wτ)[ ]csin2θexp(wτcosθ)cos(wτsinθ)ω2exp(-ρ)cosδ/(σ 2+ω2)=

ratio/c=3.51767E-43

sin2θexp(-wτcosθ)cos(wτsinθ)[QR] Qω2exp(-iρ)cosδ/(σ 2+ω2)=

0

0

0

0

0

8.6906E-12

1.7775E-13

9.01944E-46

5.41125E-05

1.84475E-47#DIV/0!
3.40911E-43

electron[QI]

Qsin2θcos(wτcosθ)cos(wτsinθ) -i Qsin2θsin(wτcosθ)cos(wτsinθ)q = M τsinθ/Q R

00

6.20472E-27

3.09797E-26#DIV/0!
1.45364E-19

π/2×0.00000002927 57

4.59862E-08

9.40559E-10

2.52542E-38

1515.137282

5.16527E-40

3.40911E-43

1.73731E-19

8.67425E-19

1.45364E-19

π/2×0.00001312066853

2.06099E-05

4.21536E-07

5.07261E-33

304333202.6

1.03751E-34

3.40911E-43

3.48959E-14

1.74233E-13

1.45364E-19

0.001

0.001

2.04531E-05

1.19421E-29

7.16469E+112.44252E-31

3.40911E-43

8.21527E-11

4.10183E-10

1.45364E-19

0.001001

0.001001

2.04735E-05

1.1966E-29

7.17903E+11

2.44741E-31

3.40911E-43

8.23171E-11

4.11004E-10

1.45364E-19

0.001005

0.001005

2.05554E-05

1.20618E-29

7.23652E+11

2.46701E-31

3.40911E-43

8.29763E-11

4.14295E-10

1.45364E-19

0.00101

0.00101

2.06576E-05

1.21821E-29

7.3087E+11

2.49162E-31

3.40911E-43

8.3804E-11

4.18428E-10

1.45364E-19

0.001020.001022.08622E-05

1.24245E-29

7.45414E+11

2.5412E-31

3.40911E-43

8.54717E-11

4.26754E-10

1.45364E-19

0.00105

0.00105

2.14758E-05

1.31661E-29

7.89907E+11

2.69288E-31

3.40911E-43

9.05734E-11

4.52227E-10

1.45364E-19

0.00110.00112.24984E-05

1.44499E-29

8.66927E+11

2.95545E-31

3.40911E-43

9.94048E-11

4.96321E-10

1.45364E-19

0.00120.00122.45437E-05

1.71966E-29

1.03172E+12

3.51723E-31

3.40911E-43

1.183E-10

5.90663E-10

0.00150.0015

3.06796E-05

2.68696E-29

1.61205E+12

5.49567E-31

3.40911E-43

1.84844E-10

9.22911E-10

1.45364E-19

0.002

0.002

4.09062E-05

4.77682E-29

2.86587E+129.77007E-31

3.40911E-43

3.2861E-10

1.64073E-09

1.45364E-19

0.003

0.003

6.13593E-05

1.07478E-28

6.4482E+12

2.19826E-30

3.40911E-43

7.39371E-10

3.69163E-09

1.45364E-19

8.18124E-05

0.004

0.004

1.14634E+13

3.90801E-30

0.005

0.005

0.000102265

2.98548E-28

1.79115E+13

6.10623E-30

3.40911E-43

2.05379E-09

1.02544E-08

1.45364E-19

0.01

0.01

0.000204531

1.19415E-27

7.16433E+13

2.4424E-29

3.40912E-43

8.21483E-09

4.10163E-08

1.45365E-19

0.05
π/32

0.05

π/8

π/4

2.98186E-26

1.78889E+15

6.09883E-28

3.40911E-43

3.40928E-43

1.31443E-09

2.05099E-07

6.56288E-09

1.02418E-06

1.45364E-19

1.45386E-19

0.09817477

0.002007979

1.14558E-25

6.87161E+15

2.34307E-27

3.40978E-43

7.87611E-07

3.9345E-06

1.4545E-19

0.12

0.002454374

1.70754E-25

1.02415E+16

3.49245E-27

3.41011E-43

1.17363E-06

5.86433E-06

1.45492E-19

0.15
π/16

0.001022655

1.91072E-28

1.45364E-19

5.43522E-27

3.41068E-43

0.17

0.003477033

3.40251E-25

2.04015E+16

6.95919E-27

3.41112E-43

2.33654E-06

1.16841E-05

1.45622E-19

0.196349541

0.004015967

0.003067969

4.51736E-25

2.6574E-25

2.70807E+16

1.59359E+16

9.23939E-27

3.4118E-43

3.10028E-06

1.82558E-06

1.55112E-05

9.12591E-06

1.45708E-19

1.45565E-19

0.25

0.005113296

7.23638E-25

4.33595E+16

1.48006E-26

3.41347E-43

4.95905E-06

2.48426E-05

0.3

0.006135967

1.02773E-24

6.15456E+16

2.10202E-26

3.41539E-43

7.03106E-06

3.52741E-05

1.4617E-19

0.35

0.007158645

1.37593E-24

8.23432E+16

2.81421E-26

3.41766E-43

9.39444E-06

4.72129E-05

1.46463E-19

0.392699082

0.008031998

1.45923E-19

1.70412E-24

1.01917E+17

3.48545E-26

3.41988E-43

1.16124E-05

5.84587E-05

1.46749E-19

0.47

0.009613103

2.35728E-24

1.40788E+17

4.82136E-26

3.42455E-43

1.59972E-05

8.08209E-05

1.47355E-19

0.55

0.01124944

3.08927E-24

1.84199E+17

6.31851E-26

3.43027E-43

2.08589E-05

0.000105847

1.48103E-19

0.63

0.012885807

3.84547E-24

2.28845E+17

7.86518E-26

3.4369E-43

2.58127E-05

0.000131654

1.48976E-19

0.71

0.014522208

4.58893E-24

2.72491E+17

9.38579E-26

3.44444E-43

3.05974E-05

0.000156969

1.49978E-19

0.785398163

0.016064515

5.24184E-24

3.10544E+17

1.07212E-25

3.4524E-43

3.47039E-05

0.000179136

1.51045E-19

0.81

0.016567766

5.43872E-24

3.21949E+17

1.11239E-25

3.45517E-43

3.59183E-05

0.000185804

1.51419E-19

0.84

0.017181446

5.66499E-24

3.35003E+17

1.15867E-25

3.45867E-43

3.72958E-05

0.000193455

1.51894E-19

0.87

0.017795133

5.87385E-24

3.4699E+17

1.20138E-25

3.4623E-43

3.85453E-05

0.000200502

1.52388E-19

0.90.018408826

6.0629E-24

3.57769E+17

1.24005E-25

3.46606E-43

3.96519E-05

0.000206864

1.52903E-19
1.53438E-19

0.93

0.019022526

6.22971E-24

3.672E+17

1.27417E-25

3.46996E-43

4.06007E-05

0.000212459

0.935

0.01912481

6.25518E-24

3.68631E+17

1.27938E-25

3.47062E-43

4.07425E-05

0.000213312

1.5353E-19

0.94

0.019227095

6.27995E-24

3.70019E+17

1.28444E-25

3.47129E-43

4.08793E-05

0.00021414

1.53621E-19

0.945

0.019329379

6.30401E-24

3.71366E+17

1.28936E-25

3.47195E-43

4.10113E-05

0.000214943

1.53714E-19

0.95

0.019431664

6.32735E-24

3.72668E+17

1.29414E-25

3.47263E-43

4.11383E-05

0.000215722

1.53807E-19

0.955

0.019533949

6.34996E-24

3.73927E+17

1.29876E-25

3.4733E-43

4.12602E-05

0.000216476

1.53901E-19

0.95510.019535994

6.3504E-24

3.73952E+17

1.29885E-25

3.47332E-43

4.12625E-05

0.000216491

1.53902E-19

0.95520.01953804

6.35085E-24

3.73977E+17

1.29895E-25

3.47333E-43

4.12649E-05

0.000216506

1.53904E-19

Θe0.955316618

0.019540426

6.35137E-24

3.74006E+17

1.29905E-25

3.47335E-43

4.12677E-05

0.000216523

1.53906E-19

Θe×1.00000000000001

0.955316618

0.019540426

6.35137E-24

3.74006E+17

1.29905E-25

3.47335E-43

4.12677E-05

0.000216523

1.53906E-19

0.96

0.019636234

6.37183E-24

3.75142E+17

1.30324E-25

3.47399E-43

4.13769E-05

0.000217204

1.53995E-19

0.97

0.019840805

6.41329E-24

3.77434E+17

1.31172E-25

3.47536E-43

4.15948E-05

0.000218583

1.54185E-19

0.98

0.020045376

6.45164E-24

3.79539E+17

1.31956E-25

3.47674E-43

4.17913E-05

0.000219854

1.54378E-19

0.99

0.020249949

6.4868E-24

3.81453E+17

1.32675E-25

3.47815E-43

4.1966E-05

0.000221016

1.54572E-19

10.020454522

6.51866E-24

3.83171E+17

1.33327E-25

3.47956E-43

4.21184E-05

0.000222065

1.5477E-19

1.047197551

0.02142007

6.62183E-24

3.88467E+17

1.35437E-25

3.48645E-43

4.252E-05

0.000225399

1.55734E-19

1.07

0.02188656

6.64181E-24

3.89254E+17

1.35845E-25

3.48989E-43

4.25156E-05

0.000225989

1.5622E-19

1.1

0.022500304

6.63604E-24

3.88399E+17

1.35728E-25

3.49454E-43

4.23002E-05

0.00022567

1.5688E-19

1.12

0.022909471

6.61085E-24

3.86573E+17

1.35212E-25

3.49772E-43

4.20184E-05

0.000224731

1.57332E-19

1.15

0.02352323

6.53926E-24

3.81854E+17

1.33748E-25

3.50259E-43

4.13796E-05

0.000222171

1.58031E-19

1.170019129

0.023932798

6.46785E-24

3.77326E+17

1.32288E-25

1
π/3

B

3.50592E-43

4.0804E-05

0.00021966

1.5851E-19

1.23

0.025159962

6.1329E-24

3.56733E+17

1.25437E-25

3.51627E-43

3.83276E-05

0.000208035

1.60012E-19

1.23788593

0.025321305

6.07467E-24

3.53206E+17

1.24246E-25

3.51767E-43

3.79152E-05

0.000206026

1.60217E-19
1.61071E-19

1.27

0.025978354

5.8017E-24

3.36778E+17

1.18663E-25

3.52347E-43

3.60196E-05

0.000196636

1.351

0.02763565

4.8419E-24

2.79846E+17

9.90319E-26

3.53881E-43

2.96398E-05

0.000163814

1.37

0.028024409

4.55713E-24

2.63108E+17

9.32075E-26

3.54255E-43

2.78003E-05

0.000154113

1.63924E-19

1.47

0.030070582

2.65474E-24

1.52385E+17

5.42977E-26

3.5632E-43

1.58878E-05

8.95641E-05

1.67093E-19

1.48

0.030275207

2.42552E-24

1.39143E+17

4.96094E-26

3.56535E-43

1.44869E-05

8.18104E-05

1.67428E-19

4.47706E-26

3.56752E-43

1.49

2.18894E-24

1.25495E+17

1.30475E-05

7.38123E-05

1.67767E-19

1.50.030684459

1.94494E-24

1.11438E+17

3.978E-26

3.5697E-43

1.15695E-05

6.55678E-05

1.68109E-19

1.51

0.030889086

1.69345E-24

9.69688E+16

3.46363E-26

3.5719E-43

1.00528E-05

5.70752E-05

1.68455E-19

1.52

0.031093716

1.43442E-24

8.20855E+16

2.93383E-26

3.57411E-43

8.49752E-06

4.83326E-05

1.68804E-19

1.53

0.031298346

1.16778E-24

6.67854E+16

2.38848E-26

3.57635E-43

6.90353E-06

3.93382E-05

1.69157E-19

1.54

0.031502978

8.93484E-25

5.10662E+16

1.82745E-26

3.57859E-43

5.27086E-06

3.00903E-05

1.69514E-191.55
π/2×0.999999999890292

0.030479832

1.63358E-19

6.11464E-25

3.49256E+16

3.58086E-43

3.59952E-06

1.56

0.031912246

3.21668E-25

1.83613E+16

6.5791E-27

3.58314E-43

1.88952E-06

1.08273E-05

1.70238E-19

1.570796327

0.032133177

0.031707611

5.20762E-33

297053484.5

1.06512E-34

1.25063E-26

3.58562E-43

3.0519E-14

1.75238E-13

2.05872E-05

1.70635E-19

1.69874E-19

π/2×0.999999999996476

1.570796327

0.032133177

1.67268E-34

9541320.76

3.42115E-36

3.58562E-43

9.80268E-16

5.62862E-15

1.70635E-19

π/2×0.999999999999999
π/2

1.570796327
1.570796327

0.032133177
0.032133177

4.2111E-38
1.85114E-39

2402.098484
105.5929078

8.613E-40
3.78616E-41

3.58562E-43
3.58562E-43

2.4679E-19
1.08485E-20

1.41705E-18
6.22914E-20

1.70635E-19
1.70635E-19

Case D(wτ=48.901915)

ωτθωτ= wτsinθ

value of [ωτ]0

π/2×0.00000000000553261063[M τsinθ][ v ] cω2exp(+ρ)cosδ/(σ 2+ω2)=ωτsinθexp(-ρ)cosδ=wτsin2θexp(-wτcosθ)cos(wτsinθ)θ=asin(ωτ/wτ)[ ]csin2θexp(wτcosθ)cos(wτsinθ)ω2exp(-ρ)cosδ/(σ 2+ω2)=

ratio/c=3.51767E-43

sin2θexp(-wτcosθ)cos(wτsinθ)[QR] Qω2exp(-iρ)cosδ/(σ 2+ω2)=

0

0

0

0

0

8.6906E-12

1.77715E-13

8.93187E-46

5.4611E-05

1.82649E-47#DIV/0!
3.34454E-43

electron[QI]

Qsin2θcos(wτcosθ)cos(wτsinθ) -i Qsin2θsin(wτcosθ)cos(wτsinθ)q = M τsinθ/Q R

00

6.49809E-27

3.09069E-26#DIV/0!
1.37454E-19

π/2×0.00000002927 57

4.59862E-08

9.40375E-10

2.5009E-38

1529.094888

5.11412E-40

3.34454E-43

1.81945E-19

8.65386E-19

1.37454E-19

π/2×0.00001312066853

2.06099E-05

4.21454E-07

5.02336E-33

307136752.5

1.02723E-34

3.34454E-43

3.65458E-14

1.73823E-13

1.37454E-19

0.001

0.001

2.04491E-05

1.18261E-29

7.23069E+112.41833E-31

3.34454E-43

8.6037E-11

4.09219E-10

1.37454E-19

0.001001

0.001001

2.04695E-05

1.18498E-29

7.24516E+11

2.42317E-31

3.34454E-43

8.62092E-11

4.10037E-10

1.37454E-19

0.001005

0.001005

2.05513E-05

1.19447E-29

7.30318E+11

2.44258E-31

3.34454E-43

8.68996E-11

4.13321E-10

1.37454E-19

0.00101

0.00101

2.06536E-05

1.20638E-29

7.37603E+11

2.46694E-31

3.34454E-43

8.77664E-11

4.17444E-10

1.37454E-19

0.001020.001022.08581E-05

1.23039E-29

7.52281E+11

2.51603E-31

3.34454E-43

8.95129E-11

4.25751E-10

0.00105

0.00105

2.14716E-05

1.30383E-29

7.97184E+11

2.66621E-31

3.34454E-43

9.48558E-11

4.51164E-10

1.37454E-19

0.00110.00112.2494E-05

1.43096E-29

8.74914E+11

2.92618E-31

3.34454E-43

1.04105E-10

4.95154E-10

1.37454E-19

0.00120.0012

1.04122E+12

3.4824E-31

3.34454E-43

1.23893E-10

5.89275E-10

1.37454E-19

0.00150.0015

3.06736E-05

2.66087E-29

1.6269E+12

5.44125E-31

3.34454E-43

1.93583E-10

9.20741E-10

1.37454E-19

0.002

0.002

4.08982E-05

4.73044E-29

2.89227E+12

9.67332E-31

3.34454E-43

3.44148E-10

1.63687E-09

1.37454E-19

0.003

2.45389E-05

1.70296E-29

1.37454E-19

0.003

6.13473E-05

3.34454E-43

7.7433E-10

3.68295E-09

1.37454E-19

0.004

0.004

8.17964E-05

1.89216E-28

1.1569E+13

3.86931E-30

3.34454E-43

1.37658E-09

6.54745E-09

1.37454E-19

0.005

0.005

0.000102245

2.95649E-28

1.80765E+13

6.04576E-30

3.34454E-43

2.1509E-09

1.02303E-08

1.37454E-19

0.01
0.05
π/32

π/16

0.01

2.41822E-29

3.34455E-43

8.60324E-09

0.001022455

2.95291E-26

1.80537E+15

6.03844E-28

3.34471E-43

2.14798E-07

1.02177E-06

1.37474E-19

0.002007587

1.13446E-25

6.93491E+15

2.31987E-27

3.3452E-43

8.2487E-07

3.92526E-06

1.37532E-19

0.120.002453894

1.69096E-25

1.03358E+16

3.45787E-27

3.34552E-43

1.22916E-06

5.85056E-06

1.3757E-19

0.15

0.003067369

2.6316E-25

1.60827E+16

5.38139E-27

3.34608E-43

1.912E-06

9.10447E-06

1.37636E-19

0.17

0.003476353

3.36948E-25

2.05894E+16

6.89028E-27

3.34652E-43

2.44718E-06

1.16567E-05

1.37688E-19

π/4

3.24716E-06

1.54748E-05

1.37455E-19

9.1479E-27

3.34718E-43

0.005112297

7.16612E-25

4.3759E+16

1.46541E-26

3.34882E-43

5.19431E-06

2.47844E-05

1.37961E-19

0.3

0.006134768

1.01775E-24

6.21125E+16

2.08121E-26

3.3507E-43

7.36511E-06

3.51915E-05

1.38185E-19

0.007157245

2.73302E+16

4.09198E-08

0.25
0.35
π/8

4.4735E-25

7.23033E+13

2.17649E-30

0.05

0.004015182

1.18255E-27

6.5076E+12

0.09817477

0.196349541

0.000204491

1.06435E-28

1.37766E-19

1.36257E-24

8.31018E+16

2.78634E-26

3.35293E-43

9.84157E-06

4.71025E-05

1.38451E-19

0.392699082

0.008030428

1.68757E-24

1.02856E+17

3.45093E-26

3.3551E-43

1.21661E-05

5.83222E-05

1.38711E-19

0.47

0.009611224

2.33439E-24

1.42085E+17

4.77362E-26

3.35968E-43

1.67627E-05

8.06327E-05

1.39261E-19

0.55

0.01124724

3.05927E-24

1.85896E+17

6.25593E-26

3.36529E-43

2.18615E-05

0.000105601

1.39939E-19

0.63

0.012883287

3.80813E-24

2.30954E+17

7.78729E-26

3.3718E-43

2.70598E-05

0.00013135

1.4073E-19

0.71

0.014519369

4.54437E-24

2.75001E+17

9.29283E-26

3.3792E-43

3.20843E-05

0.000156608

1.41638E-19

0.785398163

0.016061374

5.19094E-24

3.13405E+17

1.0615E-25

3.387E-43

3.6401E-05

0.000178726

1.42604E-19

0.81

0.016564526

5.38591E-24

3.24915E+17

1.10137E-25

3.38972E-43

3.76786E-05

0.000185379

1.42943E-19

0.840.017178086

5.60998E-24

3.3809E+17

1.14719E-25

3.39315E-43

3.91286E-05

0.000193014

1.43373E-19

0.87

0.017791653

5.81681E-24

3.50187E+17

1.18949E-25

3.39671E-43

4.0445E-05

0.000200046

1.4382E-19

0.90.018405226

6.00402E-24

3.61066E+17

1.22777E-25

3.4004E-43

4.1612E-05

0.000206395

1.44286E-19

0.93

0.019018807

6.16921E-24

3.70583E+17

1.26155E-25

3.40422E-43

4.26139E-05

0.000211979

1.4477E-19

0.935

0.019121071

6.19443E-24

3.72027E+17

1.26671E-25

3.40487E-43

4.27637E-05

0.000212829

1.44853E-19

0.94

0.019223335

6.21896E-24

3.73429E+17

1.27172E-25

3.40553E-43

4.29084E-05

0.000213655

1.44936E-19

0.945

0.0193256

6.24279E-24

3.74787E+17

1.27659E-25

3.40618E-43

4.3048E-05

0.000214457

1.45019E-19

0.95

0.019427864

6.26591E-24

3.76102E+17

1.28132E-25

3.40684E-43

4.31824E-05

0.000215235

1.45103E-19

0.955

0.019530129

6.2883E-24

3.77373E+17

1.2859E-25

3.40751E-43

4.33114E-05

0.000215987

1.45188E-19

0.95510.019532174

6.28874E-24

3.77398E+17

1.28599E-25

3.40752E-43

4.33139E-05

0.000216002

1.4519E-19

0.95520.01953422

6.28918E-24

3.77423E+17

1.28608E-25

3.40753E-43

4.33165E-05

0.000216017

1.45191E-19

Θe0.955316618

0.019536605

6.28969E-24

3.77452E+17

1.28618E-25

3.40755E-43

4.33194E-05

0.000216034

1.45193E-19

Θe×1.00000000000001

0.955316618

0.019536605

6.28969E-24

3.77452E+17

1.28618E-25

3.40755E-43

4.33194E-05

0.000216034

1.45193E-19

0.96

0.019632394

6.30995E-24

3.78598E+17

1.29033E-25

3.40817E-43

4.34351E-05

0.000216714

1.45273E-19

0.97

0.019836925

6.35101E-24

3.80911E+17

1.29872E-25

3.40952E-43

4.36661E-05

0.00021809

1.45445E-19

0.98

0.020041457

6.38899E-24

3.83036E+17

1.30649E-25

3.41088E-43

4.38747E-05

0.000219359

1.45619E-19

0.99

0.020245989

6.4238E-24

3.84968E+17

1.31361E-25

3.41225E-43

4.40604E-05

0.000220519

1.45795E-19

10.020450522

6.45535E-24

3.86702E+17

1.32006E-25

3.41364E-43

4.42227E-05

0.000221566

1.45974E-19

1.047197551

0.021415881

6.55752E-24

3.92046E+17

1.34095E-25

3.4204E-43

4.46561E-05

0.000224894

1.46845E-19

1.07

0.02188228

6.5773E-24

3.92841E+17

1.345E-25

3.42378E-43

4.46574E-05

0.000225484

1.47284E-19

1.1

0.022495904

6.57159E-24

3.91978E+17

1.34383E-25

3.42834E-43

4.4439E-05

0.000225167

1.47879E-19

1.12

0.022904991

6.54665E-24

3.90135E+17

1.33873E-25

3.43145E-43

4.41484E-05

0.000224231

1.48287E-19

1.15

0.02351863

6.47575E-24

3.85373E+17

1.32423E-25

3.43624E-43

4.34855E-05

0.000221678

1.48918E-19

1.170019129

0.023928118

6.40504E-24

3.80803E+17

1.30977E-25

3.4395E-43

4.28861E-05

0.000219174

1.4935E-19

1
π/3

B

1.23

0.025155042

6.07333E-24

3.6002E+17

1.24194E-25

3.44965E-43

4.02997E-05

0.000207577

1.50704E-19

1.23788593

0.025316354

6.01568E-24

3.5646E+17

1.23015E-25

3.45102E-43

3.98683E-05

0.000205574

1.50889E-19

1.27

0.025973273

5.74535E-24

3.39882E+17

1.17487E-25

3.45671E-43

3.78838E-05

0.000196206

1.51657E-19

1.351

0.027630245

4.79487E-24

2.82425E+17

9.80509E-26

3.47175E-43

3.1193E-05

0.000163459

1.53716E-19

1.37

0.028018929

4.51287E-24

2.65533E+17

9.22841E-26

3.47543E-43

2.92616E-05

0.00015378

1.54225E-19

1.47

0.030064701

2.62896E-24

1.53789E+17

5.37598E-26

3.49568E-43

1.67373E-05

8.93731E-05

1.57072E-19

1.48

0.030269286

2.40196E-24

1.40426E+17

4.91179E-26

3.49779E-43

1.52628E-05

8.16361E-05

0.030473871

2.16768E-24

1.26652E+17

4.4327E-26

3.49991E-43

1.37476E-05

7.36553E-05

1.57677E-19

1.50.030678457

1.92604E-24

1.12465E+17

3.93858E-26

3.50206E-43

1.21914E-05

6.54286E-05

1.57984E-19

1.51

0.030883045

1.677E-24

9.78626E+16

3.42931E-26

3.50421E-43

1.05942E-05

5.69542E-05

1.58295E-19

1.52

3.50639E-43

8.95595E-06

4.82303E-05

1.58608E-19

1.53

0.031292225

1.15644E-24

6.7401E+16

2.36481E-26

3.50858E-43

7.27666E-06

3.9255E-05

1.58924E-19

1.54

0.031496817

8.84805E-25

5.15369E+16

1.80935E-26

3.51078E-43

5.55628E-06

3.00268E-05

1.59244E-191.55
π/2×0.999999999890292

1.57373E-19

1.49

0.031087634

0.03170141

1.42049E-24

8.28421E+16

2.90476E-26

6.05525E-25

3.52475E+16

3.7948E-06

2.05438E-05

1.59567E-19

1.56

0.031906004

3.18543E-25

1.85305E+16

6.51392E-27

3.51524E-43

1.99222E-06

1.08045E-05

1.59893E-19

1.570796327

0.032126893

5.15704E-33

299791839.4

1.05457E-34

1.23824E-26

3.51767E-43

3.513E-43

3.21814E-14

1.7487E-13

1.60249E-19

π/2×0.999999999996476

1.570796327

0.032126893

1.65657E-34

9630036.525

3.38753E-36

3.51767E-43

1.03374E-15

5.61724E-15

1.60249E-19

π/2×0.999999999999999
π/2

1.570796327
1.570796327

0.032126893
0.032126893

4.83467E-38
8.47795E-39

2810.517619
492.844946

9.88647E-40
1.73366E-40

3.51767E-43
3.51767E-43

3.01697E-19
5.29048E-20

1.63939E-18
2.87478E-19

1.60249E-19
1.60249E-19

1/1 ページFig.3

z
P sinωjτ
P cosωjτ

P

ω jτ
y

x

file://C:\Documents%20and%20Settings\新美\デスクトップ\F.I.T\yoko.host\gaps-t.web\gaps-t.fig... 2005/12/13

1/1 ページ

file://C:\Documents%20and%20Settings\新美\デスクトップ\F.I.T\yoko.host\gaps-t.web\gaps-t.fig... 2005/12/13

1/1 ページ

file://C:\Documents%20and%20Settings\新美\デスクトップ\F.I.T\yoko.host\electron.web\electron... 2005/12/15

1/1 ページ

file://C:\Documents%20and%20Settings\新美\デスクトップ\F.I.T\yoko.host\electron.web\electron... 2005/12/15

1/1 ページ

file://C:\Documents%20and%20Settings\新美\デスクトップ\F.I.T\yoko.host\electron.web\electron... 2005/12/15