10
10
131
1413
131
_
3
103
R
i
j
k
l
R
i
j
k
l
x
+
y
+
z
⏟
versus
x
+
y
+
z
⏟
(
_
a
b
)
‾
∫
0
1
ⅇ
x
⁢
ⅆ
x
x
+
y
+
z
x
+
y
+
z
x
+
y
+
z
x
+
y
+
z
(
a
b
)
sin
x
2500
m
3
s
2500
km
3
/s
sin
2
x
=
1
−
cos
2
x
‖
c
→
‖
2
=
‖
a
→
‖
2
+
‖
b
→
‖
2
MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaauWaaeaaceWGJbGbaSaaaiaawMa7caGLkWoadaahaaWcbeqaaiaaikdaaaGccqGH9aqpdaqbdaqaaiqadggagaWcaaGaayzcSlaawQa7amaaCaaaleqabaGaaGOmaaaakiabgUcaRmaafmaabaGabmOyayaalaaacaGLjWUaayPcSdWaaWbaaSqabeaacaaIYaaaaaaa@4704@
n=
log
v
1
−
log
v
2
log
t
1
−log
t
2
MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOBaiabg2da9maalaaabaGaciiBaiaac+gacaGGNbGaamODamaaBaaaleaacaaIXaaabeaakiabgkHiTiGacYgacaGGVbGaai4zaiaadAhadaWgaaWcbaGaaGOmaaqabaaakeaaciGGSbGaai4BaiaacEgacaWG0bWaaSbaaSqaaiaaigdaaeqaaOGaeyOeI0IaciiBaiaac+gacaGGNbGaamiDamaaBaaaleaacaaIYaaabeaaaaaaaa@4CB4@
F
s
=
A
a
·
σ
¯
o
MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaBaaaleaacaqGZbaabeaakiabg2da9iaadgeadaWgaaWcbaGaaeyyaaqabaGccqWIpM+zcuaHdpWCgaqeamaaBaaaleaacaqGVbaabeaaaaa@4033@
M
z;pl;d
(1−
(
N
s;d
N
pl;d
−
a
1
1−
a
1
)
2
)
MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamytamaaBaaaleaacaqG6bGaae4oaiaabchacaqGSbGaae4oaiaabsgaaeqaaOGaaiikaiaaigdacqGHsislcaGGOaWaaSaaaeaadaWcaaqaaiaad6eadaWgaaWcbaGaae4CaiaabUdacaqGKbaabeaaaOqaaiaad6eadaWgaaWcbaGaaeiCaiaabYgacaqG7aGaaeizaaqabaaaaOGaeyOeI0IaamyyamaaBaaaleaacaaIXaaabeaaaOqaaiaaigdacqGHsislcaWGHbWaaSbaaSqaaiaaigdaaeqaaaaakiaacMcadaahaaWcbeqaaiaaikdaaaGccaGGPaaaaa@501B@
M
z;pl;d
1−
(
N
s;d
N
pl;d
−
a
1
1−
a
1
)
2
MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamytamaaBaaaleaacaqG6bGaae4oaiaabchacaqGSbGaae4oaiaabsgaaeqaaOGaaiikaiaaigdacqGHsislcaGGOaWaaSaaaeaadaWcaaqaaiaad6eadaWgaaWcbaGaae4CaiaabUdacaqGKbaabeaaaOqaaiaad6eadaWgaaWcbaGaaeiCaiaabYgacaqG7aGaaeizaaqabaaaaOGaeyOeI0IaamyyamaaBaaaleaacaaIXaaabeaaaOqaaiaaigdacqGHsislcaWGHbWaaSbaaSqaaiaaigdaaeqaaaaakiaacMcadaahaaWcbeqaaiaaikdaaaGccaGGPaaaaa@501B@
q=1,03
1−
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y;s;d
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y;pl;d
)
2
MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyCaiabg2da9iaaigdacaGGSaGaaGimaiaaiodadaGcaaqaaiaaigdacqGHsislcaGGOaWaaSaaaeaacaWGwbWaaSbaaSqaaiaabMhacaqG7aGaae4CaiaabUdacaqGKbaabeaaaOqaaiaad6eadaWgaaWcbaGaaeyEaiaabUdacaqGWbGaaeiBaiaabUdacaqGKbaabeaaaaGccaGGPaWaaWbaaSqabeaacaaIYaaaaaqabaaaaa@4A85@
ℕ
MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeSyfHukaaa@3759@
(
1
-
1
)
1
-
1
)
(
1
-
1
x
+
a
/
b
-
1
-
1
a
+
b
0
1
1
2
x
D
sin
sin
⁡
x
1
+
...
+
n
π
ⅈ
ⅇ
2
0.123
1,000,000
2.1e10
0xFFEF
MCMLXIX
twenty one
2
+
3
⁢
ⅈ
1 2
π
ⅇ
+
<
≤
<=
++
∑
.NOT.
and
⁢
(
a
+
b
)
[
0
,
1
)
f
⁡
(
x
,
y
)
x
⁢
y
f
⁡
(
x
)
sin
⁡
x
m
1
⁣
2
ⅆ
ⅆ
x
x
→
maps to
y
Theorem 1:
 
    
/* a comment */
there exists
δ
>
0
such that
f
⁡
(
x
)
<
1
x
2
+
=
2
⁢
x
+
y
-
z
(
x
,
y
)
(
a
b
)
a
b
c
d
1
x
3
+
x
3
=
1
x
3
+
x
3
1
+
5
2
(
a b
)
(
a b
)
Unrecognized element: mfraction;
arguments were:
1 + 5
and
2
C
|
C
|
ℂ
x
+
y
+
z
x
+
y
+
z
x
+
y
+
z
x
+
y
+
z
( x )
(
x , y
)
x + y + z
f
⁡
x
y
a
n
⁢
i
(
x
+
y
)
2
x
^
versus
x
^
x
+
y
+
z
‾
versus
x
+
y
+
z
‾
∫
0
∞
versus
∫
0
∞
F
1
0
⁡
(
;
a
;
z
)
(
1
0
0
0
1
0
0
0
1
)
(2.1)
E
=
m
⁢
c
2
8.44
⁢
x
+
55
⁢
y
=
0
3.1
⁢
x
-
0.7
⁢
y
=
-
1.1