Hybrid-III 05%


[PDF]Hybrid-III 05% - Rackcdn.comhttps://8bd730766c473bba5f62-39017777f15f755539d3047328d4a990.ssl.cf3.rackcdn...

5 downloads 80 Views 1MB Size



,

















































!

-

"

$

#

!



)

$

%

'



&















'

(

*



!



















)























































*













+







*



















































MADYMO Quality Report QHybridIII05-120531

Table of contents 1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1

2

Dummy Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 External dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Mass measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 3 5

3

Experiments . . . . . . . . . . . . . . . . . 3.1 Tests overview . . . . . . . . . . . 3.2 Descriptions of the tests . . . . . . 3.2.1 Full tests . . . . . . . . . . . . . . . 3.2.2 Head component tests . . . . . . . 3.2.3 Neck component tests . . . . . . . 3.2.4 Thorax component tests . . . . . . 3.2.5 Abdomen_pelvis component tests 3.2.6 Pelvis component tests . . . . . .

. . . . . . . . .

7 7 10 10 14 14 19 22 25

4

Rating of the validation set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Overall test results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29 29

5

Comparison of results . . . . . . . 5.1 Range plots . . . . . . . . . 5.1.1 Dummy signals . . . . . . . 5.1.2 Additional dummy signals 5.1.3 Environment signals . . . . 5.2 CPU Time comparison . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

47 47 47 48 48 49 49 49 50 50 52

B Signal results . . . . . . . . . . . . B.1 Signals of Full tests . . . . B.2 Signals of Head tests . . . B.3 Signals of Neck tests . . . B.4 Signals of Thorax tests . . B.5 Signals of Abdomen tests B.6 Signals of Pelvis tests . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. 55 . 55 . 87 . 88 . 171 . 197 . 204

. . . . . . .

. . . . . .

. . . . . . . . .

. . . . . . . . . . .

. . . . . . .

. . . . . .

. . . . . . . . .

. . . . . . . . . . .

. . . . . . .

. . . . . .

. . . . . . . . .

A Rating Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.1.1 Rating a MADYMO dummy model . . . . . . . . . . . . . . . . A.1.2 Comparing two scalar values . . . . . . . . . . . . . . . . . . . . A.1.3 Comparing two signals . . . . . . . . . . . . . . . . . . . . . . . A.1.4 Adding scores . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.2 Additional information on calculation of dummy rating scores A.2.1 Comparing two scalar values . . . . . . . . . . . . . . . . . . . . A.2.2 Adding scores . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.2.3 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.3 Results for more complex examples . . . . . . . . . . . . . . . . . . . . . . .

. . . . . .

. . . . . . . . .

35 35 35 41 42 45

. . . . . . .

. . . . . .

. . . . . . . . .

. . . . . .

. . . . . . .

. . . . . .

. . . . . . . . .

. . . . . .

. . . . . . .

. . . . . .

. . . . . . . . .

. . . . . .

. . . . . . .

. . . . . .

. . . . . . . . .

. . . . . .

. . . . . . .

. . . . . .

. . . . . . . . .

. . . . . .

. . . . . . .

. . . . . .

. . . . . . . . .

. . . . . .

. . . . . . .

. . . . . .

. . . . . . . . .

. . . . . .

. . . . . . .

. . . . . .

. . . . . . . . .

. . . . . .

. . . . . . .

. . . . . .

. . . . . . . . .

. . . . . .

. . . . . . .

. . . . . .

. . . . . . . . .

. . . . . .

. . . . . . .

. . . . . .

. . . . . . . . .

. . . . . .

. . . . . . .

. . . . . .

. . . . . . . . .

. . . . . .

. . . . . . .

. . . . . .

. . . . . . . . .

. . . . . .

. . . . . . .

. . . . . .

. . . . . . . . .

. . . . . .

. . . . . . .

. . . . . .

. . . . . . . . .

. . . . . .

. . . . . . .

. . . . . .

. . . . . . . . .

. . . . . . .

. . . . . . .

i

MADYMO Quality Report QHybridIII05-120531

2

Dummy Properties

Dummy Properties

This section shows the comparison of the dummy properties between the simulation models and the specifications. The comparison is made for the external dimensions and the mass measurements according to the specifications described in "User’s Manual for the Small Adult Female Hybrid III Test Dummy: July 1999".

2.1

External dimensions

This section shows the result of the external dimensions for the simulation models. The models were positioned according to the specification (see the picture below). Additional planes were added and contacts were defined. The penetrations found are measures for the dimensions. The reference values of the H-point height and distance to seat back dimensions are used to position the reference planes of the rigid seat. From these two planes most of the dimensions are determined. Remark: the geometry of the quality models is defined in such a way that it represents the geometry of the hardware dummy accurately. This applies for both ellipsoid and facet models. For obvious reasons, however, it might happen that the ellipsoid approach shows negligible deviations with respect to the specifications.

.

/

0

1

2

3

4

5

6

7

8

9

3

2

:

;

<

=

/

>

3

:

?

/

@

:

?

?

3

9

1

A

?

A

3

B

/

C

B

;

9

/

@

:

D

@

2

9

E

3

3

<

<

/

A

?

@

/

=

F

>

@

=

3

<

3

MADYMO Quality Report QHybridIII05-120531

3

Experiments

Experiments

For the validation and rating of the model, many experiments have been used. This chapter presents the descriptions of the experiments that are used for the quality rating. The information is as complete as possible, but is restricted to non-confidential data. In the first section, all experiments used for the rating are listed in tables. These tables contain 8 columns. Below you can find the description of the column headers: ID = Identification number #F = number of loading signals (forces and moments/torques) measured #P = number of positional signals (displacements and rotations) measured #V = number of velocity signals measured #A = number of acceleration signals measured #I = number of injury values rated In the second section of this chapter, more detailed descriptions are presented in order to give the reader more insight into the validation set. For tests that originally were conducted by clients, this detailed description is not printed because of confidentiality reasons; no extra information with respect to these tests can be supplied.

3.1

Tests overview

All experiments that have been used to calculate the rating in the report are listed in the tables below. The total experimental validation set is divided into different categories. Each table represents a different category. The ID of the test includes a reference to the category: F = full dummy test, H = head component test, N = neck component test, T = thorax component test, A = abdomen/pelvis component test, P = pelvis component test, G

;

H

<

ID F1 F2 F3 F4 F5 F6

F7 F8 F9

3

I

5

6

.

1

<

<

9

3

?

9

?

Description Full dummy test, belted dummy on rigid sled Full dummy test, belted dummy on rigid sled Full dummy test, belted dummy on rigid sled Full dummy test, belted dummy on rigid sled Sled test, belted dummy on rigid seat Sled test, belted dummy on rigid seat with obstacle Sled test, belted dummy on padded seat with obstacle Sled test, belted dummy on padded seat with obstacle Sled test, belted dummy on rigid seat with airbag

Conditions Velocity 14 m/s Velocity 14 m/s Velocity 14 m/s Velocity 14 m/s velocity 11 m/s velocity 11 m/s

#F 4 4 4 3 2 2

#P #V #A 1 9 1 9 1 9 1 9 1 8 1 8

#I 3 3 3

velocity 11 m/s

2

1

8

28

velocity 11 m/s

2

1

8

28

velocity 11 m/s

2

1

8

28

28 28

7

Experiments

.

/

0

1

2

3

I

5

4

MADYMO Quality Report QHybridIII05-120531

J

3

;

9

A

;

:

<

@

;

=

B

3

<

<

K

<

L

M

N

1

>

>

O

?

3

;

9

3

=

/

:

?

<

3

=

P

/

9

E

2

/

0

/

=

?

3

;

9

;

9

9

Q

R

5

K

2

L

F6 This is a frontal sled test with a dummy seated on a rigid seat with separate shoulder and lap belt. A rigid obstacle is mounted on the seat at 0.295 m from the seat cross point (figure 3.3 (l)) . A 8% strain belt is used with a pretension of 100 N to eliminate belt slack. The dummy wears a cotton 100% T-shirt and pants. The rigid seat is covered with a thin teflon plate and has a wooden padded seat back and a memory (TEMPUR) foam padded headrest. A seat pan load cell is mounted under the seat as showed in figure 3.3 (l). The seat and seat back are two disconnected parts. A foot plane is mounted on the sled. The shoes are restrained in the forward direction thanks to a perpendicular plate fixed to the foot plane. The sled pulse is a modified ECE 16 pulse with a peak deceleration of 22g. This test is performed to investigate the dummy pelvis motion. The dummy global motion and pelvis motion are recorded by on-board cameras. Figure 3.3 (r) shows the experiment test set-up.

.

/

0

1

2

3

I

5

I

J

3

;

9

A

;

:

<

@

;

=

B

3

<

<

K

<

L

M

N

1

>

>

O

?

3

;

9

3

=

/

:

?

<

3

=

P

/

9

E

2

/

0

/

=

?

3

;

9

;

9

9

Q

R

5

K

2

L

F7 This is a frontal sled test with a dummy seated on a rigid seat with separate shoulder and lap belt. A DUMO SG75/70 foam pad with a rigid obstacle is mounted on the seat (figure 3.4 (l)). The obstacle is positioned at 0.195m from the seat cross point. A 8% strain belt is used with a pretension of 100 N to eliminate belt slack. The dummy wears a cotton 100% T-shirt and pants. The rigid seat is covered with a thin teflon plate and has a wooden padded seat back and a memory (TEMPUR) foam padded headrest. A seat pan load cell is mounted under the seat as showed in figure 3.2 (l). The seat and seat back are two disconnected parts. A foot plane is mounted on the sled. The shoes are restrained in the forward direction thanks to a perpendicular plate fixed to the foot plane. The sled pulse is a modified ECE 16 pulse with a peak deceleration of 22g. This test is performed to investigate the dummy pelvis motion. The dummy global motion and pelvis motion are recorded by on-board cameras. Figure 3.4 (r) shows the experiment test set-up.

12

MADYMO Quality Report QHybridIII05-120531

4

Rating of the validation set

Rating of the validation set

All signals of all tests have been numerically rated in the way as described in the appendix. The table below lists the combined values of all tests. Note that component scores include all tests, but only the signals that are measured in the component are included in the calculation of the score. Combined signals are also given.

4.1

Overall test results

The overall score of the model and its main components, is given below. G

;

H

<

3

S

5

6

T

;

9

/

:

0

2

3

?

1

<

9

?

D

@

2

9

E

3

>

@

=

3

<

1

?

/

:

0

9

E

3

U

Group Total Full tests Head tests Neck tests Thorax tests Abdomen tests Pelvis tests

G

;

H

<

3

S

5

4

T

;

H

<

3

S

5

I

T

;

H

<

3

S

5

S

Group Total Full tests

X

V

B

2

/

9

3

2

/

@

:

;

9

/

:

0

2

3

?

1

<

9

?

D

@

2

9

E

3

>

@

=

3

<

1

?

/

:

0

9

E

3

U

3

;

V

9

/

>

3

B

2

/

Weight

9

/

:

0

2

3

?

1

<

9

?

D

@

2

9

E

3

>

@

=

3

<

1

?

/

:

0

9

E

3

W

/

D

;

B

B

2

/

Weight

0.0790 0.0088 0.5351 0.2281 0.0614 0.0877

@

>

H

/

:

3

=

2

;

9

/

:

0

2

3

?

1

<

9

?

D

@

2

9

E

3

>

@

=

3

:

<

O

9

3

2

/

@

:

@

:

Model 73.1% 79.5% 100.0% 70.0% 74.9% 67.9% 93.7%

0.0790 0.0088 0.5351 0.2281 0.0614 0.0877

;

@

Model 71.3% 75.2% 87.7% 70.7% 76.2% 51.8% 78.5%

0.0790 0.0088 0.5351 0.2281 0.0614 0.0877

Group Total Full tests Head tests Neck tests Thorax tests Abdomen tests Pelvis tests

G

;

Weight

Group Total Full tests Head tests Neck tests Thorax tests Abdomen tests Pelvis tests

G

3

9

3

2

/

@

:

@

:

<

M2 72.3% 74.1% 80.0% 70.7% 72.8% 71.1% 80.3%

<

O

M2 73.4% 81.9% 100.0% 70.3% 73.5% 73.2% 91.6%

O

Model 57.7% 55.7% 81.2% 56.0% 59.2% 51.2% 71.5%

M2 58.8% 57.7% 76.4% 56.0% 60.1% 73.5% 64.7%

Model 66.6% 68.4%

M2 67.5% 69.5%

<

Weight

0.0790

29

MADYMO Quality Report QHybridIII05-120531

5

Comparison of results

Comparison of results

This chapter shows results that are obtained directly from the experiments and simulations. Range plots are shown in the first section. A rangeplot provides information on the range in which the model has been evaluated, for each signal separately. By adding lines indicating the level of correlation, the range plots also provide information about the quality of the prediction of a certain signal. The last section of this chapter contains information about the runtimes of the simulations. This gives the user an impression of what can be expected when running their own applications. Time history plots of all signals are given in Appendix B. With these the engineer can visually judge the quality of the simulation results. It also helps to interpret the rating results presented earlier in this report, since the rating value can now be compared with the visual information from the curves. For this purpose, the rating values are printed below each curve. For tests used to develop this model that have been conducted by customers, the curves are not printed because of confidentiality reasons. The information from these confidential tests is printed in the rangeplots as a single dot for each test (peak levels only) and the signals are included in the calculation of the rating as well.

5.1

Range plots

In this section, all rangeplots are presented. The range plots show the results of a particular signal over different tests. The peak value of the signal during a simulation is represented by a point in the graph. The horizontal location of the point is proportional to the experimental test signal peak. In general this corresponds to the test severity. The vertical position is proportional to the simulation peak results. If the simulation reproduces the signals of the experiment exactly, the point is on the 100% line which is the line at 45 degrees, printed with a solid line type in the graphs. If the point with a positive value is below this line, the simulation has a lower peak than the experiment, which indicates an underprediction of the simulation. When it is above the line then the simulation over-predicts. Two additional lines are drawn in each plot. If the point is within the cone drawn by the dotted lines, the peak score is above 80%. Each result in the rangeplots is shown using a coloured marker. Table 1.1 in the Introduction chapter lists all markers used in this report. The rangeplots have been divided over three sections. In the first section, the rangeplots are presented that refer to signals measured with the standard sensors in the dummy. The second section adds the non-standard sensor signals (also dummy signals). The third section adds the signals that refer to environment (non-dummy) measurements, like belt forces, impactor signals, etc.

5.1.1

Dummy signals

This section shows the range plots derived from the standard sensor signals of the dummy. The plots are arranged top-down: from the head to the feet of the dummy.

35

MADYMO Quality Report QHybridIII05-120531

Comparison of results

Y

\

Y

Y

Y

p

[

[

Y

Y

Y

Y

e e

^ ^

d

d

c c

Y

a a

b

b

` `

Z

Y

Y

Y

^ ^

_

_

] ]

[

Y

o

Y

Y

o

Z

Y

Y

Y

[

Y

Y

Y

\

Y

Y

Y

p

[

Y

Y

o

.

/

0

1

2

3

q

5

S

T

;

:

0

3

g

A

<

h

@

i

9

j

@

k

l

D

i

?

/

m

[

Y

Y

Y

Y

p

o

p

f f

g

h

i

j

k

l

i

m

n

n

0

:

;

<

r

3

B

V

s

A

t

.

2

B

u

K

<

3

D

9

L

M

T

;

:

0

3

A

<

@

9

@

D

?

/

0

:

;

<

r

3

B

V

s

A

t

v

@

>

w

K

2

/

0

E

9

L

Y

y

Y

Y

x

Z

y

e e

^ ^

d

d

c c

Y

Y

a a

b

b

` `

^ ^

_

_

] ]

Z

o

Y

o

y

Y

x

Y

o

Y

o

/

0

1

2

3

q

5

q

T

y

;

:

0

3

g

A

<

h

@

i

9

j

@

k

l

i

D

?

m

o

/

o

y

f

:

;

<

r

3

B

V

s

A

t

v

@

>

z

K

<

3

D

9

L

M

T

Y

Y

;

:

0

3

A

<

@

y

y

y

n

0

Y

Z

Y

Z

Y

Y

x

f

.

Y

Y

Y

x

9

@

g

D

h

?

i

/

j

0

k

:

l

i

;

<

m

n

r

3

B

V

s

A

t

v

@

>

u

K

2

/

0

E

9

L

Y

x

Z

Y

Y

Y

Y

e

e

^

^

d

d

c

c

Y

a

b

a

b

^

_

`

`

o

^

_

Y

Y

Y

Y

Y

Y

x

]

]

Z

Y

Y

Y

o

Z

o

Z

Y

Y

Z

Y

Y

Y

Y

Z

Y

f

.

/

0

1

2

3

q

5

{

T

;

Y

Y

Y

Y

o

o

o

:

0

3

A

g

<

@

h

9

i

@

j

D

k

l

i

?

/

m

0

:

;

<

r

3

B

V

|

@

P

t

.

2

B

w

K

<

3

D

9

L

M

T

;

:

0

3

A

<

@

9

@

D

?

Y

Y

Y

Y

g

/

0

Y

Y

x

x

f

n

h

:

i

j

;

k

<

l

i

r

m

3

n

B

V

|

@

P

t

.

2

B

z

K

2

/

0

E

9

L

37

MADYMO Quality Report QHybridIII05-120531

B

Signal results

Signal results

In this Appendix the signals of all the tests are presented. Signals that are missing have been removed for reasons of confidentiality.

B.1

Signals of Full tests

Y

}

y

Y

Y

y

Y

Y

“

„

y

Z

Y

y

ƒ ƒ

‚ ‚

ƒ

ƒ

Z

Y

€ €





y

Y

b

b

~ ~





Y

Z

Y

o

[

Y

Z

Y

Y

y

[

Y

Y

Z

Y

Y

…

.

/

0

1

2

‰

‰

Š

‹

Œ







Š

‹

Œ



3

•

5

6

G

3

Ž

Ž

?

Š

Ž

Œ

Š

Ž

Œ

9

k

l

i

†

∫ ∫

.

6

?

/

0



l

‡

Ž



:

‘

;

Š

Ž

Œ

Š

’

Œ

<

k

l

i

†

l

‡

ˆ

ˆ

Σ Σ

–

3

;

=

t



‰





—

Š



Š

B

Œ

’

‰

‹





Š

Š



Œ

‘

Œ

‰

’

Š





”

Š

∫ ∫

Œ

Ž

Œ

Œ

B

T

K

<

L

M

G

3

?

9

.

6

?

/

0

:

;

<

–

Z

Y

Y

x

p x

p

…

3

;

Y

Y

Y

Y

Y

Y

=

t

—

B

B

w

K

2



’



Š

‘

”

Š

Σ Σ

Œ

‘

Œ

‰

”

‰

Š



‘

Š

Œ



Œ

L

Y

y

“

˜

x Z

Y

ƒ

y

ž

Ÿ

œ



ƒ

‚

ƒ



€



›

Y

Y

b

ƒ

~



š

Z



Y

o

y

Y

o

[

Y

Z

Y

Y

.

/

0

1

2

3



Ž

Š

’

Œ



Ž

Š

™

Œ

•

5

4

‰



G

3

?

”

Š

‘

Š

9

’

k

.

i

∫ ∫

Œ



l

Œ

6

?

/

0

:

†

l

‡

’



Š

’



Š

;

Y

[

Y

<

™

…

Σ Σ

–

Œ

3

;

=

t

—



‰



Š



B

Š

B

”

Œ

‘

Œ

u



‘

‰

K

<

L

M

G

3

?

9

.

6

?

/

0

:

;

Š



<

‰

Š

r



Œ

™



Œ

3



B

V

s

A

t

Ž

.

Š

Ž

Š

2

k

‹

Œ

B

l

i

∫ ∫

Œ

w

K

2

‰



†



l

Š



Y

x

p

ˆ

Œ

‰

Z

Y

Y

x

p

…

Y

x

Y

‡

‘

Š

‰

Œ

Œ

ˆ

Σ Σ

‰



‰

Š

‘

™

Š

Œ

Ž

Œ

L

55

MADYMO Quality Report QHybridIII05-120531

Y

 

Y

Signal results

[

x

Y

Y

Y

Y

Y

Y

Y

Y

Y

y

“

^

Y

¤

 

Y

Z

ƒ

£

ž

Ÿ

Y

x



 Ÿ

Ÿ

c d

c d

ƒ

ƒ

b

b Y

y





_

¢

_

¢

Y

Y

 

Y

Z

o

¡

Y

[

Y

Z

Y

Y Z

Y

Y

¡

Y

[

Y

Y

Y

x x

… …

.

/

0

1

2

‰



Š



‹

Š

3

‹

™

•

5

Œ



Œ



S

q

R

G

3

‘

Š

‹

Ž

l

i

∫ ∫

Œ

Š

?

k

‹

9

Œ

U

4

?

/

0

†

l

‡



‘

Š

‹

Œ





Š

‹

Œ

:

;

<

¥

k

l

i

†

l

‡

ˆ

ˆ

Σ Σ

>

A

;

B

9

‰

Ž

Š

‰

‘

@

™

Š

2

‰

”





Š

’

Œ

™

Œ





Š

‹

∫ ∫

Œ

Œ

‰

Š



’

Š

‘

Œ

Œ

t

N

/

?

K

<

L

M

G

3

?

9

U

4

?

/

0

:

;

<

¥

>

Y

 

Y

[

Y

 

Y

Z

A

;

B

9

@

2

t

.

2

B

w

K



”



Š

Ž

2



Š

Σ Σ

Œ



Œ

‰



‰

Š

Ž

‘

Š

Œ



Œ

L

Y

“

^

ƒ

‚

¤

£

ƒ



Ÿ



Ÿ

c d

c d

ƒ

Y

Y

Y

ƒ

o

x

b

Y

b





_

¢

_

¢

Z

Y

Y

Y

Y

 

Y

Z

o

o

Z

Y

Y

¡

Y

[

Y

.

/

0

1

2

’

Š



Œ



’

Š

‰

Œ

3

•

5



S

q

Y

x



6

Y

G

3

”

Š

™

Œ

”

Š

™

Œ

?

9

¡

Y

[

Y

Y

x

…



Z

Y

Y

Y

x

k

l

i

∫ ∫

U

I

?

/

0

†

l

‰

”

Š

‰

‹

Š

:

;

‡



…

ˆ

Σ Σ

Œ

™

Œ

<

¥

>

A

;

B

9

‰ ‰

‰

Š

™

‰

@

Š

™

2

Š

‘

Œ

‘

Œ

”





Š



l



’

Š

”

Œ

t

—

B

B

w

K

<

L

M

G

3

?

9

U

I

?

/

0

:

;

<

¥

>

A



;



B

9

Š

@



Œ

2

i

∫ ∫

Œ

Œ

‰ ‰

k

t

N

/

?

†

‰

l

‰

‰

Š

‹

K

2

‡

”

Š



ˆ

Σ Σ

Œ

Œ

‰



‰

Š



‰

Š

Œ

‘

Œ

L

Y

y

Y

“

“

ƒ

ƒ

ž

Ÿ

‚

Y

Y

Y

ƒ

Y

x





Ÿ

Ÿ

c d

c d

Y

Y

Y

Y

Y

Y

ƒ

ƒ

o

Y

Y

x

Y

b

b y





_

¢

¢

_

Y

Z

o

Z

Y

Y

¡

Y

[

Y

Y





.

/

0

1

2

3

’

•

Š

Š

‹

’

5

S

Œ



”

Š

™

Œ

Œ



”

Š

™

Œ

q

4

G

3

?

9

U

¡

Y

[

Y

Y

x

…

‰

Z

Y

Y

x

k

l

∫ ∫ I

?

/

0

:

i

†

l

‡

‰

™

Š



Œ

‰

™

Š

‘

Œ

;

<

¥

>

…

ˆ

Σ Σ A

;

B

9

@

‰



‰

Š

‰

2

Š

t

‹

Œ

‘

Œ

.



™

Š



2

B

w

K

<

L

M

G

3

?

9

U

S

?

/

0

‰

:

Š

;

’

Œ

’

Œ

<







¥

>

A

;

B

Š

”

9

™

Š

@

k

Œ

2

t

i

∫ ∫

Œ



l

—

B

B

w

†







Š



K

l

Ž

Š

2

‡

Œ

Ž

Œ

ˆ

Σ Σ

‰

‘

‰

Š



™

Š

Œ

”

Œ

L

205