A simulation study of models for combinations of random loads.
72
Transcript of A simulation study of models for combinations of random loads.
££ff -
IF0R'a
NAVAL POSTGRADUATE SCHOOL
Monterey, California
THESISA SIMULATION STUDY OF MODELS
FORCOMBINATIONS OF RANDOM LOADS
byIloh, Jang Kab
September 1984
Thesis Advisor: P. A. Jacobs
Approved for public release; distribution unlimited
T222990
UNCLASSIFIEDSECURITY CLASSIFICATION OF THIS PAGE fWhen Data Entered)
REPORT DOCUMENTATION PAGE READ INSTRUCTIONSBEFORE COMPLETING FORM
1. REPORT NUMBER 2. GOVT ACCESSION NO. 3 RECIPIENT'S CATALOG NUMBER
4. TITLE (and Subtitle)
A Simulation Study of Models for
Combinations of Random Loads
5. TYPE OF REPORT ft PERIOD COVERED
Master's Thesis;September 1984
6. PERFORMING ORG. REPORT NUMBER
7. AuTHORfij
Nph, Jang Kab
B. CONTRACT OR GRANT NUMBERS.)
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Naval Postgraduate SchoolMonterey, California 93943
10. PROGRAM ELEMENT, PROJECT, TASKAREA ft WORK UNIT NUMBERS
II. CONTROLLING OFFICE NAME AND ADDRESS
Naval Postgraduate School
Monterey, California 93943
12. REPORT DATE
September 198413. NUMBER OF PAGES
60t«. MONITORING AGENCY NAME & ADDRESSf// different from Controlling Office) 15. SECURITY CLASS, (of thie report)
Unclassified15a. DECLASSIFICATION/ DOWNGRADING
SCHEDULE
16- DISTRIBUTION STATEMENT (of this Report)
Approved for public release; distribution unlimited.
17. DISTRIBUTION STATEMENT '0/ (he abstract entered In Block 20, It dltterent trom Report)
18. SUPPLEMENTARY N'OT^S
r
i '9 KEY WORDS (Continue on reverse aide if necessary and Identity by block number)
Constant LoadShock LoadFirst-passage Time
'20. ABSTRACT (Continue on reverse aide If necessary and Identify by block number)
This thesis describes a model for a combination of random loads actingupon a physical structure, such as a building or ship. The various loadsrepresented in a model might be winds, tidal effects, or even earthquakes orsnow loading. Asumptotic results are given for the first-passage time for theload combination process to exceed a given stress level exceeding structuralstrength. The accuracy of using the asymptotic results to approximate thefirst-passage time, or time to structural failure, distribution is assessedby simul ation .
DD , jam 73 1473 EDITION OF 1 NOV 65 IS OBSOLETE]
S N 0102- L c - 014- 6601UNCLASSIFIED
SECURITY CLASSIFICATION OF THIS P*GE (When Data Entered)
ABSTRACT
This thesis describes a model for a combination of
random leads acting upon a physical structure, such as a
building or ship. The various loads represented in the
model might be winds, tidal effects, or even earthquakes or
snow loading. Asymptotic results are given for the first-
passage time for the load combination process to exceed a
given stress level exceeding structural strength. The accu-
racy of using the asymptotic results to approximate the
first-passage time, cr time to structural failure, distribu-
tion is assessed by simulation.
Approved for public release; distribution unlimited
A Simulation Study of Modelsfor
Combinations of Random Loads
by
Noh, Jang KabMajor, Korea Air Force
B.S., Korea Air Force Academy, 1974
Submitted in partial fulfillment of therequirements for the degree of
MASTER OF SCIENCE IN OPERATION RESEARCH
from the
NAVAI POSTGRADUATE SCHOOLSeptember 198U
NAV< ^ /
MONTEREY. CAI ^J ' *•'
TABLE OF CONTENTS
I. DESCRIPTION OF A STOCHASTIC MODEL FOR
COMBINATIONS OF RANDOM LOADS 8
II. ASYMPTOTIC RESULTS FOR THE DISTRIBUTION OF THE
FIRST-PASSAGE TIME T x11
A. THE DISTRIBUTION OF Tx FOR LARGE X 11
B. THE TAIL OF THE DISTRIBUTION OF T x FOR
FINITE X 12
III. COMPUTER SIMULATION 16
IV. ANALYSIS OF TKF SIMULATION RESULTS 21
A. THE DISTRIBUTION OF Tx FOR INCREASING X ... 21
1. Constant and Shock Load Magnitudes
Have Identical Exponential
Distr itutions 21
2. Constant and Shock Loal Magnitudes
Have Different Exponential
Distr itutions 23
3. Arrival Rate of Shock Loads Depends
on the Constant Load Magnitude 24
4. Load Magnitudes Have a Pareto
Distribution 25
3. ^HE EXPONENTIAL TAIL OF THE DISTRIBUTION
CF Tx FOR FINITE X 26
C. CONCLUSIONS 27
V. SIMULATION ALGORITHM " 45
A. VARIABLE DEFINITION 45
B. ALGORITHM 45
APPENDIX A: COMPUTER PROGRAM 47
LIST Cr REFERENCES 59
INITIAL DISTRIBUTION IIST 60
LIST OF TABLES
A.I
A.
2
A.
3
B.1
E.2
B.3
C.1
C.2
C.3
D. 1
E.2
D.3
1.1
2.2
F. 1
F.2
G.1
Identical Exponential
Identical Exponential
Identical Exponential
Different Exponential
Different Exponential
Different Exponential
case A-1
case A-2
case A-3
case B-1
case B-2
28
29
30
31
32
33
34
case B-3
Varying Arrival Rate ( case C-1)
Varying Arrival Rate ( case C-2 ) 35
Varying Arrival Rate ( case C-3 ) 36
Pareto Distribution ( case D-1) 37
Pareto Distribution ( case D-2 ) 38
Pareto Distribution ( case D-3) 39
^ (x) and r(x) ( case E)
40
Quantiles ( case E) 41
%{x) and r*(x) ( case F)
42
Quantiles ( case F) 43
Confidence Interval in case E 44
LIST OF FIGURES
1. 1
3. 1
The Load Combination Process 10
Generating T^ 17
I. DESCRIPTION OF A STOCHASTIC MODEL
FOR COMBINATIONS OF RANDOM LOADS
Many physical structures are threatened by combinations
of loads of varying magnitudes from various sources. For
instance, bridges, piers, dams, and buildings can experience
loads frcm wind, snow, ice, tides, earthquakes, and so
forth. In many instances the total load or stress experi-
enced by a structure varies in time in an apparently random
fashion. Certain components of the loads vary ratter
slowly; others occur more nearly as impulses, such as those
associated with winds or earthquakes. The problem is to
design a structure to withstand the superposition of random
loads- from many sources with at least an approximately
understood probability.
The purpose of this thesis is to describe and investi-
gate certain simple but somewhat realistic probabilistic
loal models for use in design, and perhaps safety assessment
of structures. In this thesis we confine attention to the
superposition of just two load types; shock loads, and
constant loads. For example, winds gusts, flash floois, and
earthquakes have varying magnitudes and have relatively
short durations in comparison to the times between their
occurrences. These will be modelled as instantaneous shock
loads. Cn the other hand, snow, ice, or water accumulation,
or even the presence of slowly moving vehicles present loads
that remain nearly constant in time, occasionally changing
to new levels. These will be modeled as constant loads that
change infrequently. Throughout this investigation it will
be assumed that the effective stress exerted by several
types of loads acting simultaneously can be expressed as a
linear combination of the component loads, the load
components being treated as stochastic processes.
8
The times between changes in magnitude of the constant
load process are independently and identically distrituted
with distribution function H. The successive magnitudes of
the constant load are independently and identically distrib-
uted with distribution function F. Given the constant load
process, the shock load process is a compound Poisson
process. The successive shock load magnitudes are indepen-
dently and identically distributed with distribution func-
tion G. The conditional rate of arrival of shocks, given
that the magnitude cf the constant load process is x, is
Mix) .
let X (t) be the magnitude of constant load process at
time t; and Y(t) be the magnitude of shock load process at
time t; Z (t) =X (t) +Y ( t) is the superposition of the two loads
at time t, and M(t)=SUP Z (s) , the maximum load combination
in [C,t], see figure 1.1.
Let Tx={inf t>0: Z(t)>x } ie, the first-passage time
for the load combination to exceed a stress level x. Tx
will represent the time to failure of a structure whose
strength is x, and is subjected to a stress history
[Z(t) ; t>0} .
Gaver and Jacobs (1981) studied the above model for the
case in which the distribution H is exponential and the
shock load rate m is a constant independent of the shock
load process. Related load combination models that have
been studied include Peir and Cornell (1973) [Ref. 1] Wen
(1977) [Ref. 2] Pearce and tfen (1983) [Ref. 3].
Asymptotic results which appear in Gaver and Jacobs
(1934). and Jacobs (1984) will be described in chapter 2 for
the distribution of Tx as x-* e» and for the tail of the
distribution of Tx for finite x.
In chapter 3, a simulation program for the load
combination model will be described.
i
X(t )
i
1>
<
> •
•—•— ~w
Y(t)i
.
1 1 1 fcw
Z (t)i
t t
<ll t—L •
1
V y
. , ,.
.
Figure 1.1 The Load Combination Process.
In chapter 4, a simulation study of the use of the
asymptotic results of chapter 2 to approximate the
distribution of Tx will be described.
10
II. ASYMPTOTIC RESULTS FOE THE DISTRIBUTION OF
THE FIRST- PASSAGE TIME Tx
A. THE DISTRIBDTION CF TK FOR LARGE X
This section summarizes some of the results found in
Gaver and Jacobs (1981) [Ref. 4] for the model in which the
distribution H is exponential (x) and the shock load arrival
rate m is constant independent of the constant load process.
First, we consider the distribution function of the
maximum load combination to occur during [0,t], M (t) .
H(t)=P£M(t)<X}x
=P (M (t) <x, T ( >t} +P [M (t) <X,T, <t} (2-1)
where Ti is the arrival time of the first shock.
A renewal argument yields;
P{M(t)<x,T, >t}= e~MJ*e*Pt-Aii &*'$)) pcty)
? {M (t)< x ,T, <t} = J* *t-**dMJ* ext[-AAvGOL-w) HxCt-VJ fcAf)
where G (x) =1-G (x) .
Next take Laplace transforms with respect to t of (2-1)
.
£<*) = /.* e-^HA±) it
= Mx (g )+ Am x (£ )H x (f )
(2-2)
where
-\(S ) = /X[S^ iMGrtt-W1 F(dy) (2-3)
Hence
It seems to be difficult tc invert H ^ (£ ) for any inter-
esting choice of the distributions F (x) and G (x) . However,
useful information can still be gleaned from eguation (2-4).
First, from the defirition of T% ,
E {M (t) <x}=P (T x >t) (2-5)
Thus, H^) = /V 5 * p(Tx >t) dt (2-6)
let % ->o, in eguation (2-6) to find that
1 1
m(x)=E(Tx )=Hx(0)= Mxto)
(2-7)/ -*Mx(o)
The next result is the limiting property for the first
time the load combination process exceeds a given level x.
is exponential in the sense
____(2- 8)
The limiting distribution of Tx
that
liff E{m (x)H
Tx >t}=€-t
A *^ Ac
where x =inf {t ; F*G (t) = 1}
The prccf of this result for a more general model that
includes that of chapter 2 can be found in Jacobs (1984)
[Ref. 5].
B. THE TAIL OF THE DISTRIBUTION OF Tx FOR FINITE X
In this section we will summarize results for the asymp-
totic behavior of P (Tx >t) for large t and fixed x as t-»a>
for the model in which the distribution H is exponential and
the shock load arrival rate is constant. More details and
results for a more general model that includes that of
chapter 2 can be found in Jacobs (1984)
.
Frcm the equations (2-1) and (2-5)
p(Tx >t)= e-x*£ Ptctyj e-*** (*"W*
+ *}?e-Xi JLs£ F ave-M * i*'*>s pcTx>t-j; (2-9)
let
l (ds)= // fUi) ^-O+^oiOs ds (2-10)
* (t) = h* f«i) ^V»i {<- e<*+«™W) (2-11)
1 <" >
=IT ?<**) tt^T) (2" 12)
The renewal equation (2-9) gives;
P(Tx >t)=g(t)+ Jo€lUs) H x (t-s) (2-13)
where g (t) = j* f^cdy.) e"^ +>u ^ Cx "^3 * (2-14)
Following the development in Feller (1971;" page 376)
[Ref. 6 ] it will be assumed that there exists a number %such that
i= J; exw * UH) (2-15)
12
This roct is unique and since the distribution of I is
defective, is positive.
Let
L*(ds)= e*WS L(ds) (2-16)
g*(t)= e%(-x)i gCt; (2-17)
P* (Tx >t) = t%(xH
H K (t) (2-18)
Then
P*(Tx >t)=g*(t) + J*F*{TK >(t-s)}I*(ds) (2-19)
It is assumed that the assumption for the key renewal
theorem holds. Application of the key renewal theorem
yields
lira cX(xH ? (Tx >t) = -4 f g* (t) dt (2-20)
Rewriting the equation (2-15), the equation determining
% is
=f
xFcdy; — = (2-22)
and
= />C^; —j-j^j-jj^ (2-23)
The key renewal theorem implies;
Lim e*^*?(Tx >t) = —(2- 24)^ ro
V*^fc> 7 £ -,
Examples: l> + MaCx-¥J -^fIt appears to be difficult to solve for X analytically
in general. We will discuss the numerical computation- of 4£
for two examples. In both examples, A-M^l and the
distribution of the shock and constant load magnitudes F and
G are of the form;
F (x) = e-a*
G (x)= e-b*
13
In example 1, a=b = 1 and in example 2, a/b=2.
To compute the "k for F (x) = e"°*
let
f (*) = L*PC«l«
,G(x) = e-tx
A
where A = xx = 1.
(2-25)
Fcr model 1,
f (x) =T773gT{('^)C/-e-)
')-e-x[M'-3c+e-^-^((/^;€-*4e'x ))}
—(2-26)
forX<1 + e"x andx*1.
For X=1, f (x) has a singular point, so by using the
L' HOPITAI RUL3 [ Ref . 7]
lim f(x) = Lim g'(x)/h'(x)
where g &) ^ s the numerator and h(x) is the denominator
cf the function f(X).
For % =1
,
f (1)=-£ (e*-e'x)
(2-27)
For model 2,
+ e~itx
[^(/-^f-^)-A((/'3c)€-^4e- t>x
)]} (2-28)
for % <1+e"kx and ft *1.
For^=1 f (X) has also singular point, so by using the same
method as used in model 1;
forX =1
(2-29)
Differentiation of the equation (2-25) gives
(2-30)
-,-ixZcuation (2-30) is greater than for 0<K1+e'"aRd^*1. So
the function f (x) is a monotone increasing function in the
interval 0<X<l+e~i>* . Using this result, we compute the K
from the equation (2-22) by applying the bisection method
[Ref. 8].
Using the computed x we compute the constant |f* such that;
is the constant of eguation (2-24).
14
r cr case a=b=1
,
4- _L^ 4=T7W{[ C
'- x+e"X) -Ze
"X^ (/^^"X) -T^W]
For case a/b=2,
e-* (z-*.) -3}— (2-31)
15
III. COMPUTER SIMULATION
This section describes the computer simulation model.
We denote the constant load arrival rate by x, the shock
load arrival rate by^ f the distribution of constant load
magnitude by F (x) , and the distribution of shock load magni-
tude by G(x). The simulation model will be used to study
the quality of the approximations of the distribution of Tx
by the asymptotic results described in chapter 2.
The following describes the simulation algorithm. The
stress levels are x, <x 2 <x3<- x -n
-
1, Set T = 0, N o=0.
2, Set 7=0, generate a constant load magnitude, C, and
duration interval Tc. Find the largest index i>N
such that X; <C.
Put N, equal to that index and
set
lx , =T for N <i<N, ,
set N =H, .
3, Generate a shock load magnitude, S, and a time until
the shock occurs, Ts.
4, If the shock interval does not exceed the excess life
of the constant load duration,Tc, find the largest
index i>N such that x;<C+S.
Let N, be that index.
Set Tx; =T+V+Ts for N <i<N,.
Set N =N, i V=V+Ts, Tc=Tc-Ts. Go to step 3.
5, If the shock interval exceeds the excess life time
of the constant load duration,
set T=T+Tc, go to step 2.
16
One realization cf the simulation is completed when one
T* is commuted for each level x;
, 1<i<n. Each simulation
consisted of 5000 replications. Further details are
(
z (t)
x4
x3
x2
xl
Tx3
- -Tx4 - - -
11 1
- . Tx2
I
,
Txl-I
I I
-
wt
Figure 3.1 Generating T,
included in chapter 5.
The Key subprograms are following. Other programs will
be explained by reading from the output results.
EAKDC ; generate the Tx .
CC.M ?UT ; compute the P(T*=0), true P(T*=0), sample mean,
true mean, standard deviation, coefficient of
variance.
Sample probability
P(Tx =0)= JMm^i °f T*=o is obtained fromr vx * ; Sample. j,'3€
the sample.
True protability
r(Tx =0)=1-P(Tx>0)=1-P(M(0)<x)=1- J*F(dy)=F (t) is
obtained from the equation (2-5).
The sample mean
x =xrL Tx: and
17
the true mean E(TX ) is obtained in special
cases from the equation (2-7)
.
See details in Gaver and Jacobs (1981).
Sample standard deviation
^ = T _, 1. ("fo;~"*)i s obtained from the sample,
i-
1
and
Sample coefficient of variance
CCv/J = = is obtained from the sample
mean and sample standard deviation.
CCMP ; compute the sample guantiles, and the quantiles
cf an exponential distribution with mean E(TxJ.
A sample quantile is
&. =(o<^sanple size) th order statistic of sample and
fd. - -E(T*)jfr*>( /- •<) is the quantile of exponential
distribution with mean E (Tx ) .
CCM ; compute the quantile of the sample conditional
distribution given Tx>0 and the exponential distrib-
ution with mean E (Tx ) /P (T y >0) .
The sample quantile of the conditional distribut-
ion
£o(C=[ et x (number of positive Ty ) ]th order statistic
is obtained for sample cf positive Tx .
The conditional quantile of the exponential dist-
ribution with mean E (Tx ) /P (T*>0) is
SK ; compute the 'K such that;
*={X(x): t=!?FUv x+^^.^ 3 b Y applying the
bisection method.
INT ; compute the constant J"* such that ;
A
by substituting the X found in SK.
18
The following cases were simulated.
distribution case
a , exponential 1,
(a=b=1) 2,
3,
b , exponential If
(a = 2,b=1) 2,
3,
c, exponential 1,
with varying 2,
arrival rate 3,
d,Jareto case 1,
2,
3
A -U(c)
1
2
1
1/c
1121
1-e"
ii
1-e-2X
1-/+ X
1-BfV+*P1-
G(X)
1-e-X
1-er*-x
1-e'x
/+x
1-e'x
1-e'x
1--4^x
These different settings will be referred to as case (A-1),
(A-2), (J-3), (3-1), (B-2), (B-3), (C-1), (C-2), (C-3),
(D-1), (E-2) , (D-3) respectively throughout this paper. For
each above case, we compare the asymptotic result (2-8) and
the experimental results.
The next setting is to examine the exponential approxi-
mation of the tail of the distribution of T* for finite x.
The cases of identical exponential distributions,
F(x)=G"(x)= e' y and different exponential distributions,
F (x) =e'AX G(x)=e~ fcx where a/b = 2
were considered.
The following conditions are considered.
e, A =M =1 f (x) =G (x) =e-*
f f A=m=1 F(x)=e' 2x ,G(x)=e~*
19
These different settings will be referred to as case (E) and
case (F) respectively. For each case, compute the dC , and
constant tf"
x and compare the guantiles of the asymptotic
results (2-24) to the simulated data for each level of x.
20
IV. ANALYSIS OF THE SIMULATION RESULTS
As indicated in chapter 2 the exact distribution of Tx
is difficult to obtain in general. In this chapter simula-
tion will be used to study the accuracy of the approxima-
tions of the distribution of T* by the exponential
distributions suggested by the asymptotic results of chapter
A. THE DISTRIBUTION CF T* FOE INCREASING X
The limiting result (2-8) indicated that the distribu-
tion of T* approaches the exponential as level x increases.
This result suggests that the distribution of T* can be
approximated by an exponential distribution at least for
large x. In this section this exponential approximation will
be studied via a simulation.
1 • Constant an d Shock Load Magni t udes Have Identical
Exponential Distributions
In the first collection of three models to be
considered F (x) =G (x) = e~*. The times between constant load
changes are exponential with parameter A and the shock load
arrival rate ax is a constant independent of the constant
load process.
For these cases it is possible to derive an analyt-
ical expression for E (T* ) .
In the Tables, P(Ty =0) refers to the simulated
sample probability that T* =0; X-3AE gives the simulated
21
sample irear. of T x ; ST-DEV is the simulated standard
deviation of Tx ; VAF (X-B) is the variance of the sample
mean; COEF-V is the sample standard deviation divided by the
sample mean. T P(7 X =0) is the theoretical probability that
T* = 0, ?(x) ; T x-bar is the theoretical mean of T* computed
from the equation (4-1) .
The simulated coefficient of variation in all three
cases decreases as the level x increases becoming quite
close to the theoretical exponential value of 1 when x=5.
To compare the simulated distribution of T x to the
approximating exponential distribution, quantiles from the
simulated data were computed and compared to the corre-
sponding guantiles cf an exponential distribution having
theoretical mean (4-1). The simulated quantiles were
computed as described in chapter 3. The exponential
o(-guantile is given ty
gol=-a.lr. (W)
where a is the mean of the exponential.
For each level of x, the first row in the tables
(A . 1 ) , (A. 2), (A. 3) for the quantiles of the distribution of
T x gives the quantiles of the simulated data and the second
row gives the corresponding exponential quantiles for an
exponential distribution having theoretical mean (4-1) .
Cne way the distribution of Tx differs from an expo-
nential is that it has an atom at 0. In particular,
P (T*=0) =F (x) =e~ x
for the case considered here.
Guantiles were used to coopare the simulated condi-
tional distribution of Ty given T* >0 to an exponential
distribution having mean ?, (T* ) /P (Tx >0) . The simulated guan-
tiles for the conditional distribution were computed as
described in chapter 3. These quantiles were compared to
those of an exponential distribution having theoretical mean
F(Tx) /P (Tx >0) .
22
In the tables (A.1), (A. 2) , and (A. 3) for the guan-
tiles of the conditional distribution for each level x, the
first row shows the simulated guantile and the second row
the corresponding approximating exponential guantile.
The guantiles of the simulated conditional distribu-
tion are much closer to their exponential approximation than
the guantiles for the unconditional distribution to their
exponential approximation. However the guantiles for the
unconditional distribution get closer to those of their
approximating exponential as x increases.
Comparing tables (A.1)/ (A. 2) , and (A. 3) , it appears
that increasing the arrival rate of shock or the rate of
change of the constant load magnitude decreases the guan-
tiles. The change of arrival rate of shocks appears to have
the greater effect.
2- _~2H§tant and Shock Load Magnitudes Have Different
l2£oneiltial Distributions
In the next three cases, the distribution of the
shock load magnitudes is exponential with parameter 1 and
the distribution of the constant load magnitudes is exponen-
tial with mean 0.5. The other model assumptions in tables
(B.1), (B.2), (B.3) correspond to those in tables (A.1),
(A. 2) , and (A. 3) .
As before, for each level x, the first row in the
guantile table gives the simulated guantile and the second
row gives the approximating exponential guantile using the
exponential distribution with theoretical mean. Comparing
the guantiles of T* in table (B.1) with (A.1) (respectively
(B.2) with (A. 2) and (E.3) with (A. 3) ) , it is seen that
decreasing the mean constant load magnitudes has increased
the guantiles. Further, it appears that the convergence of
the distribution of 1% to an exponential is faster in the
case of smaller mean constant load magnitude.
23
The exponential approximation to the conditional
distribution of Tx given Tx >0 has theoretical mean
E(TX )/P(T* >0) . Once again for small levels x,it appears
that the exponential approximation to the conditional
distributior of Tx is better than that for the unconditional
one.
3 • Arrival Rate of Shock Loads Depends on the Con stan t
load Magnit u de
In the next 3 cases, constant load magnitudes and
shock iDad magnitudes are exponential with mean 1. Constant
load magnitudes change according to a Poisson process with
rate 1. Given the constant load magnitude at time t is C,
the probability a shock load will arrive in the time
interval [t,t+h] is M(C) h+o (h) .
In case (C-1) the conditional shock load arrival
rate is ax[c^=C. Comparison with table (A.1) indicates that
conditional shock arrival rate x(c)~' =C has the effect of
decreasing the guantiles of Tx . Further the exponential
approximation to the guantiles of T x is not as good as in
case (A-1) .
The approximating exponential distribution to the
conditional distribution of Tx given T x >0 has a mean of
Z (Tx ) /P (Tx >0) . The guantiles of the exponential approxima-
tion to the guantiles of the conditional distribution appear
to be closer than those for the unconditional distribution.
In case (C-2) shock loads arrive with conditional
arrival rate aj^C)^ =exp (C) . Comparing the table (C.1) and
(C.2) , it is seen that the guantiles of the case ^(C)"* =C are
less than those for the case ^c(C) =exp (C) . This is because
interarrival times tends to be larger for the case
A(C)H =exp (C) . Comparing tables (A.1) and (C.2) indicates
that the exponential approximation to the guantiles of Tx is
not as good as in the case M='\
.
2U
In case (C-3) the conditional shock arrival rate is
Micf = exp (-C) . Comparing tables (C.2) and (C.3) indicates
that the quantiles fcr the case
yU{C)'1 =exj (-C) are less than those for the case ^(C)"* =exp (C)
ard furthermore the exponential approximation of Tx appears
to be close for the case (C-3) than that of for the case
(C-2) . In all of the cases the simulated mean was used as
the parameter in the exponential approximations.
4 • load Mag,ni tu des Have a Pareto Distribution
In the next three cases, the times between constant
load changes of magnitude are exponential with mean 1. Fhock
loads arrive according to a Poisson process with rate 2. In
case (D-1) the constant load magnitudes have a Pareto
distribution with parameter <*=1 and the shock load magni-
tudes are exponentially distributed with mean 1. Comparison
with table (A. 2) indicates that the Pareto constant load
magnitude has the effect of decreasing the juantiles of Tx .
Further the exponential approximation to the quantiles of Tx
is not good in the Pareto case; (the approximating exponen-
tial has a mean of the simulated sample mean).
The approximating exponential distribution of Tic
given T^ >0 to the conditional distribution has a mean of
E (Tx ) /P (T x >0) . Once again the quantiles of exponential
approximation to the quantiles of the conditional distribu-
tion appear to be closer than those for the unconditional
distr ibution.
In case (P-2) the constant load magnitudes have a
Pareto distribution with parameter o< =2. Comparing tables
(D.1) and (D. 2) it is seen that the quantiles of the simu-
lated distribution cf Tx for the caseoC=2 are larger than
those for the casec(=1. Comparing tables (D.2) and (A. 2)
indicate that the exponential approximation to the quantiles
of Tx is not as good for the Pareto case as for the
exponential case.
In case (D-3) the constant load magnitudes have
Pareto distribution with parameter o< =1 and the shock load
magnitudes have Pareto distribution with c*=1. In all three
cases the siaulated mean was used in the approximating guan-
tiles.
B. TEE EXPONENTIAL TAIL OF THE DISTRIBUTION OF Tx FOR
FINITE X
In this section simulation will be used to study the
exponential approximation
suggested by the asymptotic result
This is an approximation for P (Tx >t) for fixed finite x; it
should become more accurate as t becomes large.
Two cases are considered. In both cases shock loads
arrive according to a Poisson process with rate 1 and
constant load magnitudes change at the times of arrival of a
Poisson process with rate 1. The shock load magnitudes have
exponential distribution with mean 1. In case (E) , the
constant loal magnitude distribution is exponential with
mean 1; In case (F) it is exponential with mean 0.5.
Description of the computation of % and T* for these two
cases can be found in chapters 2,3. It can be seen from the
computed value of 3((x) and <f(x) appearing in tables, (E.1)
and (F.1) that X (x) is approaching the value 1/E(Tx) (where
F(Ty) is the theoretical mean) as x becomes larger and for, &.
the cases computed X(x)<-—: . Further , r (x) is approachingE(7x)
1 as x becomes larger.
. To study the exponential approximation to the distribu-
tion of I , cuantiles from the simulated data were compute!.
These can be found in tables (Z. 2) and (F. 2) . For each level
x, the first row presents the simulated guantile; the second
row gives the approximating ^-guantile computed by
^=~[-ln£i*(W)}] ( I )
26
The third row shows the approximating ^ -quar. tile computed by
qo( =-srx )ln(1-oO ( EL )
where the theoretical mean is used for E (Tx )
.
Comparing the quantiles in tables (E. 2) and (F.2) it can
be seen that the approximating quantiles (1) are close to
the simulated ones even for «>{~;.40. The approximating quan-
tiles computed in (jj;) do less well but improve as x becomes
larger. The two approximating quantiles approach one another
as x becomes larger, as expected. Approximating quantile (il)
has the advantage, however , of being easier to compute.
Table (G.1) presents 90 % confidence intervals for
^-quantiles with dL>0.9 for case (E) . These confidence inter-
vals were computed using a large sample approximation, see
Conover (1930; page 111-114) [ Fef . 9].
Comparison with table (E.2) suggests that the approximating
quantiles approximates the simulated ones well for these
values.
C. CCNCIDSIONS
Approximating guantile i. is always better than approxi-
mating quantile £ . Approximation I approximates q^ well for
s(,as small as 0.40. However I is more difficult to compute
than £ .
The performance of approximating quantile 2L can be
improved by chancing it to
y ' PCTx>o);
and using it to approximate the quantiles of the conditional
distribution of Ty qiven Ty>0; for the models considered
P(Tx =0) is easy to compute being equal to F (x) .
27
Zuj<mUZ—t-Kna—zHCLZUJ
—OO.KOCJ^uj
I
W
u
• rtf
kj: •H•«->
w CH-1 0)
en a< oH cu
XwHrd
U•H4->
fl
0>
13
• QUJ3(-1- UJ
c> «_ onr "5KEUJt- _><«!-•UJ ^lazr > o<a -iQ_«ex U.4 < *-
t «o>Q. •*_<~Q
1 or <>— Ht-aO_> £.£.**-!a «»< 1
Z (-I-**»/»iUO4ZOO
• 03II» u>o^>i^>
4> >—•^ ^s* e©<m fv—•m
t> rrvHHOOOOO
OOOOOO-ifNiO*OOOOOOOOO'Hoooooooooo
>jT^oir»f— On^oooin O* u~\ h") *4f f\jr^» CO'"^ <^
H» OO-HfsJi^lTV^-*
OO^rvn^N^- ,o
<x •©•oormO'O^onjinp-
CD P-VWWT^iMi'lV >r
OO^Nn>fNrr»^
i— O -OPs|f*)CD •*«"> —MOm* -O^INHOOOOOOCl ••••••••••oooooooooo
O <fNOO-f »r -4".4>CD .f »*
!_»*, «n JUy * mm --—(_> £.
f— <Omw—*OOOOO0 ^Q- oooooooooo O
O —•-^rvrgmm -* #* m
•rvcm oofN*«vrgo^omj^>a>-^o*'MO Of1*f*rs|
O co<"^m<"\|inr<»^r»*r*>r«>*J>O c -rHrft^rr)^^o* *rn'T>-nr>^)^ moco-oor"--Hnjjin*o jj-coo• •••••••••••••»•••••
h-m-^ojrgcomi/N-^m-^in-H -* *'*>fN(O r,*ACO O r,J ,,Wl/-'r*«-rOUO'J>" ,'>n.-«^"*m(^ O—4 "U «J lO -A* JJ '.T* H> -O <i"» u"\ ~« CD -* -f" Q —*'J*r<}
MO^H-rOOCMAH'>r»0<M^M(#m)r.cO
o* -rco vo"io 'TOO oo9>Nvaxo -r o */^j
0-*CD -«'M -O —<d>QCO^-*p-r>rvLM/>-«(7t O-HO* mo^«*>»rm<-«coin-^o,»co-0',»mof*>.-«r—
|
o • • • t • • • ••••—•—•—« -4r^rg gf *J •*>*©
•o *mo -«-*Nmf* -*" «"* o>m co f\j rsj co r+ —»o>co 0*"O oOO co o*» r-r- co cxmo coO0<04 <o -r• •*-* rvX307»n'V^^OOO' ,'tf,r*^ -T "*>!*>
c* •• . ...... t
OO —«—« (V—«mmm \r\ co cow rg co co r*. co^ mj
lACO'MOcO>»P*-f^>'0 ON^C*C"*fl}JNK*m (Tvcm^-t *or^^jrM^j-^^4^f»w>r-ir^^^'-*rn
O 00 00-*-*«%|rg^^ 0^>00 0^-t -r^f^^a -^ ^^^4 <M rs* rCf **>
f>» ^^rnfs-CO-*1 ^ -T-t COCO ^»00-^C7'C?* OT^rNj-^• ••••»•••••••*«•»•••O OOOO-*-«rvjrgm)'r»iO'0^0'T»fTt-^'^r\joj
O" OOOOHHH^f\<f\j4?^0-000'OOc?f
o^ <-»oo -t" i*^—•^ *n t/> -o f"»of^^ ^ co cot*q* ^^*counrr>*H>rrnr^tnoc7^»OiAtr\u*\c7v >0
»n o-^<^ -r -ocof>JTOr^^^>ro<N^r»o-^rvtr\^o
O 00 0000*^-* r*Jr\jm<n*ru"*r--cDiMc\!coco
r»-0-o<>i0^0o r,J^> l'^f—ocorgcoort>-^r*'TN-rO'N^'T >r -r*rv^^ v»orn'vm*«vn
-# O*^or«»^r «coOT orsiLHsT corner-VO'W—
f^ rs|f*-o^-*, *oeoo*ineomrg-Oo •©^•^-O
« •»•»•*••••?•*•••••••
^•OO-t^-iCUsrrg^/oncoo^^-Tnicoco-cf
CF .OOOOOOOOOO^HHf^fM^finN^
^ ,h ii>^NfO<>f*-mcomo^^m'Ocoo>0 m r*-r— in ^T •^^^^mjOrsiO^o-fmo
rj OO O^O^-h-* ^TP^co^^^^-rN/iAOC^r^O
O" OO OOOOOOOOO-<-*-<NNm'nin>0
O "^ O M»fTnr>r^ir\0 TO«""int^r»
-- t>0 c^OO-^CJOiO r'K^f>uicut^WNOCo*<JU
CJ 0000000000000 00^-*-^<-Nj(M
>ooooooooooujmou^o*no*noiAO
O* r»rsimc7»'-H^»'T>>#o-^—«»A'^-M-^fnco -o-^coO ON'O^OO'* <>f»»co(y»^)-^m'N-^^>^*coco• •••••• •*••••••••!••«
O? meof -t-f*r»OOi/>*A^rnvf\iA^^f>j-^r*>^-,—.—,—« fN* r^ rr>m^ U-y CO XJrsj ^
p4o »r» inO CO -O i^J rsj ^4^ if\^ *4 eo ^» CO (N »^»
O <J*—•f^'A -* ^V r**n» co -^ aJ p^r* **> -« *•* <D r*- ft)
«_>0-^^'«'0tf»t7»r-gw.rrnr*>u)*^,^r»^f.r>j
o <n -ra» <j co <n*n r*omr«4 unm coon# >r *><
O* <^-^coo*c^-*'inrgrt>o ,OfN4'^»nr».^)C^cof,-Nr
CO fM04-or,»0 {©0'N*'T'NO-0<N*^r'-nj<r',*r>*st.• ^^-4 0^>«n"5t r»r»vnmr*>pgrr>(T>oi>~*inm-Q
(7 •*••••••• ••••••—* -* -^-^rsi rM rf\mtnm CO CO ^rsiO^ CO t> co -*m
-*-h^h p>intni »r -r
O—•Lnr-n^'nOT'O®'-» j-O'-n^^- >^fr- o^O T>T-^^ rN' (>* cOr*'-si-H^)Ou^rsiO-OcOLn
O1 OO'^^'M'Mm^ > >h-N-00^-0 -*"-*• f*l^-4^-4-^rMfNjfn^
ry f*>m •>» r»»n >f ^O -rm^ >r <\» -o «1 *r f—*u « -* «r ««»nw» co to -»«>•-• co -^f*ir*tn •**''• r*m
h, cocO'N(rN*co«r»'^'-*-* ra-*'N'Mr>s*-*-rrnr»>gO
O oo-^'^-^-^'^i'M'*' -^-O O<^0 >f-T*-*-^f,vrg
o* rgom o1* fv o* a» '^ -o r* p* tn -o o*^ o* o> co co
• ••»•»••••»••••••»••CJ 0000-»-*rgrMrnrr»^srr^^oO'0-0'», 4'
oco<MfNj-r C'*»o^na^rn'Of^^^H^^coo ,''0>,«n m-*r*r-oo ,n^rn'Ti*tnr^rr>.^-^f*>fT>^i^»
O oOOO-^'^^^*^'^l rM p*^'^u^incOCOrMrgcOco^-•—4—«^^
^co^«MOf,*pn-^co-»-4>^^h"0*nr-0'^rnr— ui rr> i-r> co **j -r co rg ^n rg rs* rv—4 rgo rn r»- rsi *r*
*C m'T»^ntnPta-r*-*'Hr^p-trv^>f^v»{j»o-^c>co'o• •••••«•••«••#••••••
CT 000000^-<HHNN',»n«^(J'(7,n^
^o 1*1 <m nio %o in ~*inw rg -^^v h»m—«m rsi<m^finr-r-sr u^ tr>'NJLr" >4Conrtujr)U^i^inrnu^r*
wi rgrsi<^roinirtfN.«>^^rvf»-cou-\h- w-4 4*fTiLn-o• ••••••§•••••••<•••••
f^^^tnoOm cotn^ co rg co 0>o <Ntnjco co tn -^m oOiro^l^N-o«coif*tror«car*or"0
t •••••••*••••§#•%•••«CJ OOOOOOOOOO^HMMmnuM/\NN
O ODNO ^^4 0CD>0^f-'Orr»-H'*'*T> ,A r^^^r<4 .-i^rgfjn«'i >tmh»r*-0'-*'0^*4"-ocDt7v coo
• t • • • • t"••••#••%•»•••O OOOOOOOOOO^-4-4HNN<^^«*\-0
^* uo*-*—t-^-^i^rNjrnrnirMnr^cv-Hrva/cDintJO
O OOOOOOOOOOOOOOhh^^Nn
O -* -^ r-j ng
28
VIOlZUJ— XUJZOUJZOa — i_>u.
—OQ.XOUHUJ
•"•o n#»* rn^m -c a>^~ i >•-
ivD^o-D^ij o Ji^jin' *i»o^^oA'ny<
<N
CMI
U
w c-J Q)
en a*»: oH a.
*w
U•H
Ca?
-»- UJl/> <« QaC ar^uj^uj -3>— •—
I > Oa- a. ** -» *.
a. ^ _j— o»— *-^-oclj
o* «*< i
Z >-•-*:*
* OU3XX
ift -> sfrO^O-O -«-'© tft
gj -O C3* rg o »*- r\J ft -Org
ooooorg g* o^'n
ooooooooooooowoooooo
^O^COO —«f>4> ift<N
uj r* sj-tft ^ r rg.o j-*o-oO f\ ^CT -r -^ ^ .c —«r»rr)
I • • • •
t- 000-^rgrr>g> r-O-0
CO co ^o -o in -o (No g* f--
o
0C tft^tftfgccor-vorggv
00O— -.r W > OOO
oooooooooo
CDO^rg^O'O-O^CD ~
^"•' w-«oooooo ^• -Joooooooooo o
TO-to r*mOOQ* —•-* r*> 4} tft, rgo gj p- _* r*» tj»
CD -O O rs»a>o^ rsj^ coO^ a> a> rn^ rN# r>rg -^Q> rgrggjeootft g>a>rgrgcgg)-*f—cocDrg-H'x>c3
OtftrgO ^tf>r-mrnrgr*(^o«0^ T-«0-«
<J oooo-
U>rnmrf>g> Otftr,»(7*COeDOrg-Hg>tt>r-gco.t, rr)
r-» ^*rg TtftCT'Omift.fnrotft <J ^tftrorocQ -0^>O
O OOOOOO-^wrgrgromtfttftCOeorgrgcDO
0*> ^*-*^O tft*» ift IN U"*e> tftC> CO -^ CD ift CD iA.
gj o-^f">'*x;^»o-^ f*»ao ,</r*orv rT> rncoii>-*-sf
OOOOOO- (t-f-oocT'-r g*
corj*> -o ino—^^cc^io tft oto^o^®rg^OrgrngjvOcO-O'OP'''*' co-^^Oiftrn J"\
tft 0'-*"^ r^*yift's*coojr»">C^O<7*-*'0<© r^ r*0<^
O 00000000H-4HNNff|^^N.K-<0
-^ »TC0iftO'**t7*OlftC0^>r0^--^'O-^OrN;iftC7»fn-^-TtAvn>r*-o <^J4> co^iftgrgrgr^r>-
O OOOOOOOOO^^HNN^ntftHMBU)
^) rgiftrNioOf*g-^*Nco ^ »rsj^«Mift.h-o
1*1 OO0-^O <WW'T*ft'^"00>ft ^? f*>-^tft r*-0 -O
ooooooooooo-
l«1 f*>NO'OOH>ONO ,^N',l'* ^f^-wcO»ft Ift rgmr*«J-0-^OCDr*v/*fsj«r C^ff>'^C7, -Trg OOO-^O' g—•«^igru-\^)eo-^«ia?<7*ajO r, tu>
C/ OOOOOOOOOOOO-^^'H'HfM'^-t^
-— ift OrVC7s OOC7»lft'^'i*>-^OO r,,-^sC
g> O f*- O^- 3> «1 *^ CO <N -f -fm rn > rg
ooooooooooooo-
V tft tP NniNO^'T'tn^'*f*i(^o
ooooooooooooooooo-*^-^
fNO'^f*> ,MCO',ta CO«0(^'ftm'DO-0<0^ift -Oi^l
C3K3inift'g'g'g'T»V'tw»-«-^r^ y.--*- r-iQ
CO rg rrj m coO r\IO^ TV-H -0O tft i ft .^O 0^ rf>
CO tft^-^OTOf-O'-^tft'J^-^'M O'^(DHOOOH
C7 .•<•..••..•....•••OQ^^^4^rgrgmrn 1n tnp^r,^4^ r,p^. gj tn
ift iftin^rg>-o.O*JOC7»O ngO r^rnOCr, >rnrn-*rg
CT OOOO-^-*—t-^r\»M^^«0t>O-t*<N»'N~4_irgrg
OO—*rn<*g-^cor>'*>--u^-ft-^cO'<> ^rgrggjift
^- tftiftcoco f>J-^'s-^*ift<ftr-.t-*u-Mft -r ^or*o»rn
C7 0000—*-^—«-<'NfM'T>fT>tftiftcoco'vrgcoO
r- j- j- ,o .Q a*O •©-«'*• tft COOO ft -"Nj-O-Orgrrt
>*i •*** O OV^COfT>'^tr V»COCU-^n^^» 4» CT''-»X\'^
t •••#•••«••••••••«••
rgrg c*1* ^TJ^a*^ o-^ o<^»0^**- co^otn -Otf\ n>f|-T t^O«/'7t-T-J 1^|.^-^'>j(-.cor»i<r>-^-^• ••••••••%•••••§•#•%
Q* rg co C7»O -jrg -^ gj co c> rn rgco ift -^O co co ift
gr rgojmro-r»ft r*'s"OC3tntf>nm4> ti»g'g>rg(g
0>«^ <N»0^"N|>r^rgrO<>J^-Ocoa)0(Mrnr^gjntg^grtncD-^—««^cu-* ^^JtOwi^OT
m -^-^rv*-grnn^-tftf>»r*o-^^> og^tft-*r^T>^-
CJJ O000OO00OO'*'4'*-'f>"VWTn^
f»vO fr"^ ,O r^-O r^"^^ -o^*^ft<t)'^^M•^^*t7'^gift mrnCT'^r— aJCT^-OOtftV* -T'NCOrgixiftO'^rg •-•-^-^-^rg'^r^g'u-t ocot«">"tC7kUvotit-0
O OOOOOOOOOOOO^^HN'Vrt)*^
—•gjiftrgrgorg^^rg.^O-O -^O^ 1^ CO—«-*rr>-^O-t'tft-^-^-wrg^p*. g> O^rgrn-O rg^- >t (>
rg -*,-*-4-*'\|rgrni-n-l' > -0^OO^n^ ttft
r-*O rn r>* co r»> «^ -* co rgmv to -O r^* *^ tft'j* tft -*;
o oooooooooooooooo^^^
o o o o o o o o o o o o o o
O——*rgrwn-,(-i ^. g> tft
0-4<-*(Nrgrr>m^«rm •g *-4 rg rg r*i f*l
29
—XUJZ
—00. *OOX.UJ
«>• oo
mmNN^ ©r,»m'-«>oorgin'^rriP^omf«i-<?o> co-^inrgm-j'gooo.o^rgo-J'^'OVingrco
r»eorgcgVrgorg-OOCOin -OO^O-OrO*)**
w \f» -o co^m in i/* <-*mmo -T t*\-^ -«or* r»o
rg -0m <n 0> Is* r*> TO—•m r» CO —I d» rn COO CO <*> co
O CD -0 ^ -Ti rn - g rg o r/io r» CO ?3 -0 ^ —* 0> —• -*" ^
ft ••*••«*•«•••*•••••••3 r^rs*rOrOinincocors|rga>cor-.cDrripT»»nin*g^
—»—(—,.*-" jrgsj- r -o ooo—»-^
SO coo*"O oco rnco ooin in o> g^co g> -©ft> *t
v* v^ooo T,mr,"i/»rr|inr'»oin rg-^<-r**/vor,*rg
4 rg r*> n | inm UWQO
mI
• o »UJDy-t- ai
>/> <-. aocUJ»- _!<«-»UJ «ItrrZ > <J>•* •-•LJ_*«CC a^-ma.m acu>->o. «J"<U
1 «<ii- t-t-ao_> iC2«l-Ja. «< 1
Z t-l-**—
i
V>V>0(J<>:uo
• oan• uu^ko
CO •© r* <7> **r-mO -O C7* co o> cr -JO <oo <o V» -*CDm mC7"^^<^^'OmrgrNjh.r«jgr-<(^ 07*^0*^*</» O'ncT'-f *>* ^J^inconomoo-i-oor-CFNco
in <0 r» gf CO rn f*r* ^-» f*> f*- -Hr» rg rg -T *nr% gj rt>
-ro co co -*o r»mm r* -*> f*> -o <mh» r*>m c?» co>r <Ni <^ r«- o* -f-m gf rsjm -4* a*^ rsj»n r*> gf gr -^ ct»
fn^>cor*mg> g^ r -* c* >r\ —* to -o ct« to in o o^
co t7»O "1 ^H gj frin |rgom r«* r* inO 0> CD —4 <*> rry
m r-fT)g3r-io O'nHm'* gj*eo-«co**or*co>n-*O* inm<gn>m>t nviOO'^'^-^m-r'n'^OJ^O
O '^'^^cgjrnmmnco'DiN^jcoBcocomrNih.gj)-^—i —»-^' -^' g -r -# « v
mfn-OCO-O Tco-^rvp^g^ 4>Hinh <7» »n (7»^*0>v/tcomr—r^oi^co-JFO'V j-^a)i/Mf»«uinO'*l
m^o^mr^rvjtn-t -fm>*-ico\n^a»ON.O'nOrvp^-r gjg3^in-Of*>^00'COOO p^fTlro Oco id r j • g to -o r> to n "T^- -Of7-cr— -gr^OTJ T
rn
w
t fti
< •H4J
w a^n a<! oH Q<
KWH(0
U•H4->
a0)
»o
mjJ^corgdO^O^O> ocO'Ominf'^o^cocon^I rginf*>rr>o>rnor^-^^^U. O^r'^—lOOOOOO
ooooooo-*^-o>oooooooooooooooooooo
o a* •• ^ 4*m (*>»n r*>o00^0 gj o^ COO^ 0> rg-^ rs»rg in ^h -0 co 'nO -0^ n-^r*r- OOin J- -4
ac cor*-r o>>f ro-*fr>f»o< cof*>ocD'«co-«rn>«'rcd o,»coo*-*-^^co^mo>I
r-igJf0i,n>co^rgrNJj(^
OOO^njfr)tno,« >r «^
r>g t_Kn \/* <*>-^ -+jr~ n 1 1(|
tn c>»hm <-i corg ft%—« r»»
O "Orgm co >jrn-g^O
oooooooooo
r» rgrgr*.g3r*>rgjrg-^gf>inr»l g^rg;cocoi**'fc*0>r
,»C7»cOf>jr^g^gjrJNcom»f rno>—*coo>comg30
h» f-«rgjmm-^OC0c0OC7*a>-0rf>rgo^^0^-H-^-f
O OOOOH^^^fl)N-t4>NNHfH^)NO^
rsiomrnmorsjmramg3^or*0't,pr>-^ p,>coVs
-T" r* rg iv o^ u i gr r- rg*w -«r» *d -o —«»n?—t r»> ^r r* com<n rg rgtn in« » ^f fn Jf coO <*!*H
« r\jm rg g> rjroO •©O P"" r» -O rf^ p- g> rg gj«mroOrOrgrgr-inrg^ir* Oh^g^oo^rcoo^-*
tn o-^rgrr>in-o<^»o-0'0 -0<)H-^n-t»na)O'N
CT OOOOOOO-^^-grgrggf g^gagjo^Omm
rgO^-g?OOs000 3>'0'^vn'OrgrT>rr|0^noo-to-4 *rr»-*m<^ ,oo»nrgrg-^cD'*/rH
gf o^HOrgngf -<;r*-^rgco^^HO<?r**^rgorg
CJ OOOOOOOO'
-^ m^-^rOrg^Tnornmr^or-rgtnrginr* r"nrg^>aI '^r-.grr-r*nnn(/>P*iO*rgr
rn 000«-*-**rnrninr-corgr^o-*rgrgcoo>nco
(_» OOOOOOOOOO-
h- o^r^0x ^»fs»co»t, '-«P»-rr>»-*0> ,*'*»-^^r^in m nimtnr*-rr>rgogjO'>r 'gom-oo^-rg
O OOOOOOOOOOO^^^rjfMm^-O-O
>f CD *-trr>C7*ing3^<0>-OincOrT>0^ r,JCO
^ o om rf>r**t,r^u^^4rr>*NJ'0'^comoOOO -<OW -4 r?> rr) ir\r» CO rg prj O^O -*^ -O 0>
f^ ^p^oo O'Om-rr^r^r-g^in'OO'-^o^co-^in
O Oo^-^^^-^rgrgrnrnmmcocorf»f*>o>0>*00-^r>rn
coo -OOP'-rnrgm Orfi o>corrto> gfr^cog> -goU-.-a1 u lAU-v t| U ,^^,i| (ov , 1|t-.^ni U \H|
gjjgjO^CT* -Tr?>»-»-^rgrgoo> 4>- >f rgrnorgrgtn
O 0000-^-4rgrgrr>rr>mg
Of-*inr*oorging3corgcorg»rinorn'00»^r*r-oo g5>4;'V'gr»g5r*uirgcO'rin-^'^r*(/.-r r r>.r-oo o-o >T -rr-r-r- <i gr O—t-*r^-i
o oooo-
©O^trtrnrgcoo g3r«--0rr>QOOOrgrg0x g>ininmrOCT'OOrgrggj g^gf g>o ^mrgrgmr*m rorrfintnr-co^^'^aocococornritintnr-O'grg
• •••••••#•#••••#••••CJ ©oOoO©-*-^*-4^cgrg-$'*g>gDO>o,»tf%m
ro rg r* gf-o—* co *QQ >0 in in C7» C?» r^r- ^i rg rg gjOOOO co V» coO ? r» co O" -T 'OOrgr» -^r* u~t
rgrg gf pT)mu> cov/» mrr) OOrg-gr* cwrgr^ rgrg
O OOOOOOOOHHNNmrng1 ^
CO (*) CO in -^ rn f*>m g^^ »* rnO r0 <N—« -Om^Ocucur»r» -H-^-4ni rg *j v\ gj io—«rgr» r^O V -W
oooooooooo- <rgi>*mm«m
g^ co «-^ rg aj> rf» *tO roin coOmm r-on coo 0>m m>rrgrg<vrriO-^^r*>j- ,*''^cDco-^^<-<rgrnrg <•+**«»grgrt)(T>grmr»r»»-4^-«cor*r*r*«4'-4rgfT)
t #•«•••#••!•*••••••*#CJ OOOOOOOOOOHH^HfM^^tOO
rgtn rg rg gj- co ^ -Om-go in co >fO 0> ^O -r co f"»
^^h-r^mmOOr^Oco^Ocorgorgoco-*--i t-H —4 ^^ rg rg rO rr(m gj coO rr> ro •-»—* rg—« r- o>
O" OOOOOOOOOOOOH^HNffli^*^ -J 3 OOOOOOOOOOOO^H'MN'n^-t't
co cost' >Qrgo-OrgrgrgMJ —«J ^ CO -T co co ~* r*O u »•-» rsj r» -gr rg .-« -^o• ••••t«*toooooooooo
r- H H in Or-CD^inn-o-O-T -g»rgo>r«»
< rg m i^ *o<o«it'UO r* ,'tU','y>ui')Hn *^ 0OO0OO0-«0 ,X |N-T ,», «wysn«iHHJ> t I**ltltt«>t«*O © 0000000000000000-*HfMN
<0>r ^<-trT>rg«*»r*^>rorgrg^tr'CV, coorg
o ooooooooooooooho^-^nn
^rgrgromgr>rmOHHNN(^P)t^in
oooooooomo'no^O^Oi o. HHNNmnf^w
30
CQ
W-CQ<
I
CQ
0)
w(0
id•H»->
a
aoa.XW
aq;
M0)
«M«H•HQ
ZlU<-.uz-«>-WOI-ZwXUJZOUUZOu.—wa.
OOKIU
> <J
a ^ -^ *.
J *: t -i
<< I
aizououxx
0> ** -*m -» o om ~o o
ooooooo-*-*-*ooooooooo-^
Kio •*O -J- 'St so U"»^ —
•
et fNjf»-in'>jooc7»<o r'40
© ,©^N.O*'»O-*m^-0^
X ••••••••
- -om^j^oooooo— ^-(OOOOOOOOa • ••••••••oooooooooo
O * eors#rg OO'VrgrNjrsi .-,
^ n-tyooouuo<J ^w •••«••••• ^o. oc^ooooooo o
o-^-^rgtvm^^r -**n
O »^- re, _, u-, <> _«0—*^U">^D ^ (> CMW „* ir» -« C?>
<-4 1-«-^—4ro r*> ^ >f to© rs| r»> rs^ -^ia*-^^pgr\|rr>rn
-* -o (?»o <M ni -«r »no <o ao*n -t ^r i/* -o ina -* o
O -» —•O<M •*• f»-O GO 0* -O -# "Om r»—4 *0 "1 rs|oo^ >ooinfMO',,fnNinrtio*A-fi''i/*^G'noy
CT ••%••• • ••••••••*-•-^ rgrg fn >T *> -O (->O '* f*
00 >* -^ © -^ <» rg ,f f — -d ijTi^r'j^i-n f ^^lN
a » • ••*•*•••
—«-H
-*r\nr>omr\jm^m.o -o-^-^tncow<o^*"Cor>i
f* •fl-OOinocor^-ODC?'CT, maO(7*[J*'n^H^, r*rri^
«Mcgcoo*maO!>m<\ir«»Or\#Tto ^mo-O^J-Orno*rno-^«*<7**-»f"»mco'">jO^-<7'ir\'0'*»0-o
o* cyoo ** ^ "O in rn co tn o» r*-m aoin «-* ^» -^ >oy. -^) O'^ j- — r— j- ^-i/» aj ^> 'mi^i ai ai —* rn r -O
OOOO^^^^^^rgfnm*mr»coao^-J, 'nfncDa5
t «•«*•••#••••••#•••••
m 5*h"O -* *t r\tO -^ ^O ^" t>^^ <"0 •*> **> *
t •»•#%••••••••••••••a oooooo^^-*HNfn4, in<x»onmHH
^O^fneO-^rNj t a0h»^^oojg>rrih*rfK)r»>O
f>J O'-f-^'Ni TinOJCD'*>>'rim'K»(DW rtT*l'*>OT3
>oooooooooo-J • • t1 & — ^rityimm-t + m
-_—_^ <
-*—irgrgrr^rri
4>m <A rt)Q p<» o r*>i^> ni -^^ rf>m^ >orv^ra
-^*n f*> rgu> o»cn;« »rg-^fT(o ao<o C7*0 in</> -^ad
• ••••••#••••••••
o*mO'A-coof,*.ni o -^rnc^ ^aor^cD'0'O r>^»
•Ococoaof^JO^MO ft^^-OCOO ,s•0^ ^r^ojo
O* ao^ N- -* O* rs$r\(o ^*O -* -• "*"^O i>^ -^
^JflOO^NNtO /mN^IOH T -T COO TW
^roo> ^cDf\jOfnmrf>*»tf,
\ ^fpcrn 1 ^- -*f»»
^ ^r*-r»rgrgv^or^r'»rgmof»''''T* rn-r i',
» rvtn
r) m«iin<ncoco^ ^^rr><yr^o rvo r^' -o *-^*v»
rgrg-T sir— r*.^^uo(7*i^Ovuo' ,gO'Tw^'-
rj r\jrjrnrOiALnX!> -t ^^^^-^ r>jW^ rr>OT0
C7 OOOOOOOOOOH-H^NN^^ODS
OOOOOH N N
31
(Nl
CNI
CQ
Q)
W(0
o
t fd
CQ •H4->
W aJ <D
CQ art oH cu
Xw+jaQ)
U0)
*H«H•HQ
I—. _J
Ztu«*-*
Q. -UU.-oaxOOHUiO •UJ"*
o
- -J« <-*UJ m t <\ £X > -3
u. «* .j—«oI < <
-» ^ < «> _j
& <t< I
2 »-»-**
WOO* OOXI
f*»^oin rsiOin'o-*o> »--nOcoor-com*«.>f'
u. -r-400000^^0
O—• <TO -r r* r\# r. > cry .©
OOOHNO"*ND OOOOOOO-"TOC0OOOOOOOO-*^oooooooooo
O^"" CD *7> O -O <"sj 3*» tf"\ •©
-Omino^'-'O OfVNCOlT""'"--«OC>O rrir'-in
at (^^ v*ou-*m«N'*' * »r*
^ c*cu-«r*'omO'T«yco fT> rn ^» p-
) in r* as f*> *"• *»
1 n^NH ^m ct> mn> t>
X •••#••••#•OO **<Nm in co >r en a?
'""J"*-* MnrwiM"«
I C*rnco<'r> r'"m0'»m~«0 Xi— «(^t-«00OOO0«w rn-^oOOOOOOO0. t • U.OOOOOOOOOO o
LU^ -JO **" -OOrNjcococo -»
X 'fc*n ) ^»MCJ(^CJ ^.
t— n>—OUO«JOOOO <— • ••»•»•#•» _}Q. OOOOOOOOOO O
U) OOOOOOOOOO •
I » t - t • • • • •
rvj \AO >H—»O irw*) rsja>oNi <0 t+ •© **> r»"M «"* -fC?> co.ocdO'0'T'"s>w-«*-i-o O .*v/»t>'*>*reo<J*^O •~*»nf^»^rf>OrMa>0 0-^OOrr>oo*>'s-inO's"
t ••••••••••••••«•••#•3 rs*,-«fT>rr>.0U"*O(7,'iJ"\mf»m-4-#iri -OOO o <;^ HHNN#*OflOO'ON
ino »*0* -h -f r»» rn to r\jo f>* -O »*> c?» >*oN **i
o w>-*»*»"*or»pr).rinrneo'''»-«0'O lo<>s*r»^
-*m-4W ># <*1 n l *>Mlc*V"*m
^ cr> <--<"<J-^0 -O^^a-v-n**- <"vj (7* -'>—«'*- jprn,r
ip> "»o-r r>*Ooo>in'T>in rT*-^'0'nt*"C*n,r -oajo*
0* r*» en-*o-O '"**- -^*n in r\i<*>«© tr^fN-orsja* u"*f»
CJ •••»••••••••••••>••*OO—•-^rn rsl in -t <X> t* rs|r^—•o r*vom •> BD «)
oi •.••#••••••••.«..•.00-^-^*N*r>#'n'ninino>»oo -t ^ r*>fn^h*o-^
>t —* -0 tn^iA^rnrgmrso^o^o^^iAm o^-^Df^f^ooinoc^r^fMinoo-rnof^o
O OO^^H-*NNt^f*^NN^C)rg!M^fn
r* -T -j-ooommmtn-*-* ^r^^ajn^o^H^O OOOOH-^NN'f^ -o^*-•or-^-co^in^o
<t> -*o p* to to* to^*o*• h«^m cd (7*mo **
O i>jrn<J'0'^'-^i^'C^-^-^0-^*" r^-r«1'^*i^>-*
O OOOO^'^'^^'^nt/Mntoton'^'^H-tifl
t> Oh-'N'Mtnoto't o^"nOH*> t^^'*!.'^^^-.s.^ o^^Oro-o aoro^^-to^ CT-O
O OOOOOO-^t^Nn^-O^OO'flOiA-0
rg^rgi**f*-o-Ot> -f -otv»^mraom«n^^4vn,-n tr- rNj V r*<0>»'*>CO-r-*lJ*COrgr'>^-00
o oooooo-4-i^-<NfM>r'rNpT*vD^
-^ O f*> D> —* nl-*<Mm >M T5 -H •©O 'J' <NO <MO
O* OOOOOOOOOO-^NN-f •* OOO^
»or\jtnrsja>-*-Oto-*-H >rsiotnfnrsj^o-4-f^-f*>-OrotO'*^^*rs)^^-^-p»Of-'J"m'Oao^5
o oooooooooo-*-*-*<M'*>'*)mmaocD
O tom-u o«^rr)^nj^.r«»f^in—iQ^y •*"
m oouov>^-•,,<'T^ ,,l«|^'/, t*«> ,' , ^ tooO OOO000OOO0OOOO*HNN«f>f
>ooooooooooiuinomov"»omou"\0X
O *n *A-h -^ -t 'Wrvi rs| c?«OW (O -^ -C •*" rs4rg (n 4>t^» o*> rn<DQ*r,'-flo-^—*-^o-o *T-0(/,r*JTtot7«r^O rr|-r (Oo-nrsi^-«^o^oo r0^">|t^.^'c> -rt •«•••••*••••>••••••••O rsjrs|n>ri>-0'0OO*n^^"»'0 ,-<'Vsnf^or^aD'^
< <» <i <
cotOK-oin,otoOtOur\0°s*rginrrto-^-^rs|»n
V tJO'^'^ntrnr^iry^inr*) - *f»s/* 0-^<0"lf*rn
O rs*r^nirr(inini**a>r^rr>fnc>*iu>(nr*^.n»-^a>r>»^*«^rs|rs*rr|pr1 «w\u»n/*^ *
<0^'0'00co rr)to^rc0s> -^rsjO rr>o'— contT-m ^aj(7n/»-TCD-^t,*rs|coin-TO>n'T»n>m-^r* -r
(/* »nin»n»n-^0'0*nin"i-^v/>-rtn>rr* r cr-«o -«
CJ -»_4rjrg ^ 4- ^> -OOOr- O^N ff> t>0*»vn rsJ-^—•-^•-•"«<>('*•^ +j <; — —
«
O ^Ht(7> OtOiA'09>intNt01irsi-4 s|t>nr*)
C7 ••••••••••••••••••#«-4-4rsj*-«m«nmiAcora->rsjfr)-*<~imrrtrr>rnao ^)
pH -* rsl rsjrn r»>mm co a)
rn-«-» n o ^>'n^rA-»ao^ro^'-H>^o-*>st, K.«0 min-^t>C0C?*rnrri'>J'O'*-O , MO-^tJ«rs*ors|rsJ
coco f«>-4^iAi^-OiriO'^ rO^OtO^'* OJ ••«••••*••• * « t •
OO -«-* <>* rs* rf| romm C*O *r *» *n **s ** *.OQ-^•*^fs*f*irn ^> />
m rnm<r*ocot>-H^^o^'Tiinin'>r<i'?iin r*'r^r» r*»^--H r,s|33r0OO (0'Or-»f0r- ,
*,»O'>JT rr»C0''-s|
O 00-*-^-*^^'*> rP*^^t'r*^*NirsiOOrvrs*-4rsi
•"*r-in«iT'«>to-*',*mrgcor>jinr-in-oo^' T^ 00000-00 0'-«-« f,,-a>'Y>0'^J^O-«-<r^t •••••••••«••»••••••O oo-*'-«-^^'M r^*'*"0'0-^-^'*- r,*cocosnin
rsi-^rs|-T"lQaDrgo's"inrs|rs|(7*in^O(>'00^*
4) sT T^f^-rs*rg^o-«—«0-^ T •* TtTV*"r»"nn
o oooo-4 -*^* rs' rrt',">u"\mcD<om'Ti-*-«JT -f.H^rsjrsirnrn
P-O r^^t0^rsF'M^'vf'>»'0-*, -0-^tO>cOt>^r*OC7'0-f-* rt^ fW^Oinrv;t7*^^r*>^*3)r>.C7, *Hm nirn^i os"tMAu»',ivraj{>'T)f> rsf'^o^^'-4
OOOOOO-^^fMfsj'O^'O OOO-O 0>A O
O -O rn ^*- r* -* rM > »-• CD C7» N* U» O*"* in rsi -H **>
r-p*.fT> 4- v*0'»rs#rs*-or^tDtD| vrv/'CO»nfr|rs|^i ^<# rw^sy o (j —,_<r»%N x> -c -g j* ~r O 1
," / ' -J
cj oooooO-^-^w+r^rsi^^r^r-fsi-^eoa*
COO^^^rs. ^ rr>>—«^— ^n-fsj-^^Nfsji/>fs|^)• W(yuO t©I>'«airstf»>^^istujOL»-H«vr-f|
-^ —t*^
LU CDrsuno—•mt?*fNlOCO*Mr«-0 O ^0>* %T *" r*^rs* <-t-* , sffv,)n^^tM^-0'O*'> o rV"^'-'* r*"'s* ***
UJ • ••••••••••••••••»•-j (j ooooooooooH^fMN-r^oooo
z< coco-^mp-vnCT'Orn-T'^w ^n'vvnt^rgco^o >©
3 -H-^c^C7t C^o^c^ln^*Ln'0's-ln^*^nlnoa^pCJ rs| _iH-4H^n * >r«»h»rvrgoo r,
sl r«J^n'">i-^ T
-i O OOOOOOOOOO^*-•nimmm into od<zo-• myivrsr-f *"«')^J'*'<Usris)-o<ii , lU»'* ,t»i'
CJ t ••••§••••Z O OOOOOOOOOOOOOO^^NN^flau >oooooooooo• ujmomo^ou^omo
1 o-"-*rgr^rnm^-rvn
32
m
rnI
—
w(0
t
CQ(0
•H-
W -^ 0>
CQ cs
< oH CI.
KwJ->
a0)
MQ»
iH4-1
•HQ
*«OHZ
Oiuzd
OUKUJCJ »w —'•* ow
O t
• o I
*-- UJ
a orzruj^UJ o—
_
»— _J< <3 —Ui «X(£ZI > o
^ cro :>
u. ^ _;—
a
a. << |
z. r-»- **
• ouii
mO-n^- O > O —»<"sjrs*
g0^in i"rt<"NJ'«"ttJ>—<Og>
-r-^oooo^ooo
OOOOOiNjininOiN
oaoooooo<-»-«
^ino^'^^'rcoco'ngj - j _.-~ '
w ^ -ri g> LP rr,
Ct rg rg n-, <j —•—»--, T -U O^ m-*^ <"*<>« l n"> tf«-tff«1
co rsj;ocoON->J''— rsjinp-
I -TOO-0-H*Na3P»-*ico
< *-»gp o\/**»*y»—•—*ijw»
— ^ti^hOOOOOO— ^hOOOOOOOOa- •• u.OOOOOOOOOO O <N
aji>oooO"'5 -O ~h-* rn r—o <0 *n r» g^co
r\* •-» rg CD -^O rg ny -O f\i rt> CO CMTk r*>O 17» P*O
m^mo •Oo,»co-*~*o>J, -oo's- -torn—»*? -j*
intor*-^r^in>r<7'r>i>roa3 0u^h.rv-r i^ -*o
gf njf*- <v -^ rr>OO O WSO r^ -« iT» f*-lA ^OO -4 J3
V*-*«4iO i»i«—•^^0»4/i*n/*n|^r-^grw/ni gp !» g*
r- ^m^m in inm wrm -g> o* rn q* rn n» rno co -*-** •••••••*•••••••••#
<j 00-^<-«'N r^-^^ r"'s**^ rN'^'0<^'*> ir^ tog
^m^th oa^-mcd^-^^O O-orn-^0,»p»pncojj^h'-g'^sfajfn^CHOH^ >rnjp»p*ot>
—«p*m'MCD'0'4>'-**nnmr\i-^Q>»w*^-«p*-
^•-g-eincDgjr**— grm-rmco-iO'O-OP-'gr-gr
3 OOOOW^'
O ^^TCDgjrsjgjc^^rNj M«rrri-<jgjgj»*^oO H-
i— pn-^oOOOt>OQL> ^* t •••••»•• • 3Q. OOOOOOOOOO o
*mro >r »f* <© <B ni -» rv ro -0 3)
c» oot>ot>o-
IflfMHN 00>K^CDlA<iO^CM)O OkACO
-^ir>^rN4fnoa>fno*-^*Atnp*' g? -rr^O'N0> r*-g^r«-«-ir<-i/>(©o-Orgfs»f,»tA-4yr^or»3>o^
-r —«o ~u i/i a* o w^j^o^vjj'jy-o-in r ^ a
-<-«n-im^0-<O-M)OO>^-<-' g*g>t^
rr> rnm g^ %rm a>—•p* r^ r*> co <n f> •*> r><ooc o>OrNJOu"\CM"vjg^m<N g3mrr»^r»r*cDO'7'f,*Wl
HW^WOOT -rnir^uif*lv/*»J*-r « -©m*nrn
g3 4>(7««0'OfNJ rD^*'00,»u^r\jff«rsjgfrnfT>-0>»,
gj OiOOiO-g^ONO'MHO •Tf^HtO^Oooooa^mocp'-^cr'rnrn-^mrga) ^ ^^^
r» <y*o of-OOOOu"tu-\r*o p,J<D prir»rNjrnr,-m
^g3cc^>rncOii^^»g3r*-u>n^ir»Lr»P*"ir» o^-r»r^jfgj--og3(ti^'^' -grorMOcor*-r*o—»-
O) ornr»rno-T'Ti-^insrr-rn^^-^ -g> «z>'nij*rvj
oo^fn^o^^jor-inu/ut-^sr ^ly^oogj o -^ -* v*O n )mm -© •-• ' ^ *» —« (/» t/» in <^gr*o
m<DP*gf-g>m-*,'inm-rinp»-rg^NO« gj^-^ajmrnf>jf*>«>-^in',*^"'ixjp*o,»^'UO -o^o-t v
•gf ninio-g3 0«-i<30Cflo-^tr'-^fT>'g/'r*-^ OLT"i> gr
O OOOOhh#-*-*rNg*^<"nm
f* O N
rng3»^rs*a0tr>'r>O,« Of>0*AinrgyO^-OCOO
rsioinp^mtDm-Oh-fNirn-c-t -to-^-^rgco -^
tr(7"4*m'^ r>*'Jrmrgcotr"^t>'tC7s mnigf»>#-o
mcocor-{7»p*JPf>'*'nj p," r^'MOf>^0'7' l^-g>
tn^f- -Op^-Oco-^-^incD-O o•4> co-J^* rmoo*-»_#rs|r^gr 4" COCO ^n rr>-^ r'J^ Ot^OfNJO 4* CD
O OOOO OOOO-^HN^r^fomoOO^'O -J 3 00000000HHNN(n«)in^OO O O
«1 ^ g;u^'«f^-^f, i^a)wi^iN'ronn/>«gf «-«i^i v*-/ag^^inc»r*(g»T- yr^r»y^gn
3 OOOOOOOOOO^^-^^rgfNgfNf p-p»
n»c_>o-^mo Tf^ornwcogjcotr-to^o^i-r
^-< oo»-«^r>jr\jmrn-<j ^oOO'^"'N"CO<Aiinr»coVa oooooooooo'
<rgr\jrrtrn-4*>4*tnO - -" N fN 0-*^rNjr^rrtm>f
33
w
I
U
w
U
CD
ft)
>•HuU
a•Ht>i
M(0
5Z ~WO zt-na, lij
~x ZOuJ O
oaiiuo • —•
O •
.2
• ORUJ^»— h- LU
*/> <^ Qa orzuj^UJ tJXh-
X. > o^ ~io-j<a. avii^ acO:»u. *-»—o
I or<*
a. «*< i
z »-»-^^
# OUII
<u<o<N "W" uj ou -r **• aj
I f».©C7-.OOOco*»<\|,*U» NO^N-*-»0000UJ • •••••««••
o^fvmr\jcDo*-o>vnQOOO--rVN -O^csjOOOOOOO—«r*K>oooooooooooooooooooo
mc*<"vjC3-4CD-*0*-*0
C>rsjr\j<-O'*t*©.jrsj«0Q
• •••••••••oOo-*m m*r\ (7» r*>-h
-4<M
u><iv"f i u * -jj >y j-
m
• •*»••••«
in c* *« n>—4 ao rv*> —•"
oooooooooo
O CCNiO>0 ONOO(DD
a. oooooooooo
X 0*H^fMrVft>fn-^N**lA
O* »A 'OO« r^O CT»« -4^ rsj -^o» co r*. j> «> f>» ft>
CJ OON-^J/ftV^iA-4^^tf»K^-4(>^-«o-t
C* Nn^'^iinnr»r.in'^'nrsOfv^f1 »-«'r>'4 a• • ••«••••••••••••••••
CJ cj)0-*^rr>fN#rv«ru*»*i*e'n'T>—•mnnn^NO4*4 rv V« K*>M *< » CO <0
CDr»r>*i> -sT O -T O^r^l^fn^^OJ-f -O -£> r»- C7>
m omr<».r>©r»rgrnn»co-^.oo*'0-<-*T*«P4 j-r*
t **••••••«•••••#•«••or ooHONH*n«^Ho«ooiAOQNi—»—• —»-^« ^'-g » -r <4#^J
mc0C0O^>V>'t-7O'4m4)N9>O^(V)^KN{> U*t*rnf'"trn-^*,*C*»-«<*>-4*^U,»(7'iT) r*>-*'$' CO -T"
CjT • •••*••••••'•••••••••0000-4-**>fM(ft^ONrt>fNJOO-40^^
—*—i r>*^-» rr» pr>^ ^
ty» to ooo r*\ **m t*\ -*»»• oxfT* co^- —4n^ -* n*o •*
t -*-^irnn-^OOCMnn-)f— T C*'"'- 0^*'*>*0'>i-<cj ••••*••••••*•*
O1 OOOOOO^H(>jMt >*n.r».-«wc*coo*aoM»4HH^^
u*>mCDrVCON*'0-4-0*0-ON»',r»<0 ^f'-OojvO'OOniQi^Ki^w v^'^i'H/Oni^V*'^ CO
cj oooooo—^NM't-ro'OoO'O'Oiftj'l ift ««JT>|
(>»noN ^co'N--« rMrMO',^'*'ru'no',>^>-4r- LU i f> JO r_j u —. — , .j (_> _« a % (— CO—• « ' f- <_, i_.
• •»*;••*•*»»••••#•, •- »
CJ 0000000--*^(*)^^^Nf*fMMiDaj
t •••••##•»#•••!••?••or oooooooo-<HNNftimm»no^^^
^ nO*m •Of*'OCJO*M^^ ^^r*>-Ornf^m-0
ooooooooo^-*-Ho**N'n'*'-©'Ooo
-* rntDtnr*>rnniaoo-^-^'Ooo-^«ON-ff'0
< •••••••fl»«*t««t««»*i<J OOOO^J^OOOOOO-^-^-^r^fti •*••* <J^"
IA --CDO-^O-^^O^-OfSCMO'^Oi'OU^CD
CJ OOOOOOOOOOOO^^HiNromiftinK
u. -^ ^- -> »*- r— rn oo^o-^No^torgoO r*J 0000-«0(Mrg^-irv*,~ajr>j'^c* >j't>0<A
O OOOOOOOOOOOOOH-HHfMN-f*UJ-J
*- t7> wi y* oo-^-^oajfnr^^aotD—4 -r^^^ u> n
i v r^ptii* -rmrvr^aj«j^-4j—iv«r«« -^ C?oaot->t->0-^O f'^^^n>rr(irMrta3i/» *r io-^3 ••tit ••••••O CF OOOOOOOOOOOOOOOOOH^N
8>oooooooooouj»nou^OW^O»nOino_J • • • • • t • t • •
1 OHHNN(tjm*^iO
0*> CO-^rsjfv.QDcocOrvaJO^u*"* on-i, o^t7>fO -^O's*f>4-^a3r^^ >f-T<N'r>-rr-C0Ofl0 r^(X>'A
^ ^n ^» <noo <N -^<n eo ^nr»» -^ <t» »n ^mr» as r«i
CD «>*-o<;nT*Jl/*u» -4Ji*cO'-"0-^"»",* »y*'-* *" Hi
• •••#•••••••»••••••••
*N <M <"N# rs<-4O ^T f>* CO sO ^^O *!^ °4»"^HI CO^0> r» J0P*>ro?*r\ ^-^'UC0 , '4'4J'^f>>Ot/t n»U>i#>-4
& Oo**'^ rN* ,M ,*Nr n*'©*"4'Or,»'Of"-'in.OOrgrNj.
tn C> p*0> CD^ i/> ^ Ht) -4 -0 O CD >TOm GO^ C7* *H
CjT ••••••••»•••••••••••OOH-#r>i-4fommmcoeon*>r\JOC*-*p**«.r-
pa|a4CV*4f*Kn^Hf
co OmO(7«tfMn^ *to \sy rry c\4—*mv +*-***•mv• *ni-nco'^"', if'>w^'^» ow,^^^^* h,^'<)
Ql •••••»••••••••••••••OOOO -*-* <*s| fMm fn iAin O^ co> »*) <M -^ **) f>
p^>4mnjrm<i
-<-0-o.eQi>oiAflO>*io-f ^ o*nm*Min-^
r» n->m-00^-4t7» (J>^-«0^'» h,00',)s^^
r-—•—*-4rs|fM
^gJ^f^om^nP>"^«'>m^-^O•»'-Hm«^<0•0aDC^tf \ O ^*» <J* •** —•» >• uji * <• i«-\ uji« itvx-r n ) aju>r»
r» »Nr>ju^inci*O'0<?^»p-<*^'N-O',*-r-yir\w-^^
o ooooo^^-^o**^^>r-o-ooooom^
corOO*>r*irs|rn'MO>O rV»^-*Am'0»0*A *^0r»o<-r'inrvri-C3*^-t^aji/'U-\ •r^-f'j"O^'0^
o oooooo^H-4Nm'n»ftm'*^fsiN^^
mrr»inroo^inc*20-^inin t ^^^^^rsioo'^-*fN in<o -tO iO f* -o <? r* a>o b o-^-^^n'^-*s- com -^-^fv^u-nr>aoo^ sfinf^^ <ja>coo'V>*^ rO
• ••••••••••••••••••••Or OOOOOOOO^HNrxrt^m'OT'^^ >f
*T rn r*> rtl "O -* -4 ^^^* -^ -^ *> -O rg aj -4 -OO CO 05
t ••••••••••••••••••••CJ 00000000-^-^-4-*<^ r>**»''*,,0>000
n*lOO -0 ^4—* -O c0—«O 0> CO -«^t> ->UMAOO
• ••^••••••••••••••••t
u. o^o^pJO^H^org-^^inn^oO^u^O—<oaoLJ m »* >c;tP'<»'r--*, »HOmmn»r^i/>0'* y*n»(7*ri.O
UJ • •••••••••••••••••••—i cj ooooooooooo^^^^NmcitfMr
z< ^o-toocoff-Hi/if-^iiin-o-•^coco'"*o3 <NJ>r--^rn5)f>J-40>O>0^**si^C0 rr>C0^4O'^>CJ rj 000-4H-^N'r»'r|tAO^ONin(>00-*0
-J O OOOOOOOOOOOO^—«hn^^ >t
o
o • ••••••••••••••••••••z O OOOOOOOOOOOOOOOO^^^N
> o o o o oui m o <n o «*>
O ^ H rg M n
34
I
U0)
w(0
u
• 0)
U 4J
w en
•< (d
H t»
•HMU
c•H>i
cd
>
v»o<Z«--)CL Z UJ
-tx 2OUJQO~OUXcj • w
>-_ UJ^ <— oa oezaoUJ OIKr- j«a——
!
UJ ^X^^x :> oa. a. < ^X.^. QtO.»a. -*_>-- tj
»- t-*-GCO—
»
-: *- i -j
Q. *< |
• oaxx
•V \S* -TO"" f I ' "* u » iw sT
| CD o ,J"» o^OCD**'*-^
ooorg -oeo-^m © •*
O OOOO-^mm OCT*
oooooooooo
O~wg rn in o* © o rgo-grgg>»—
OC -^0<~g O-O^-^g—^O
a toooooooooo
O cooog* o-o-orv-r © •-«
I— >«r'Vg-«OOOOt»>0 ^*- • • t Ja. oooooooooo o
X 0-*-*<MrNJ.rr*mNr g/«-\
OTg-^otn-orncooo-go^-m«*(m»h
3 fN*-^tf>rno*r*-ir>fnr^rnf>iprr|«>0'^<OfT»co>—•—•rg rg -* g> h- gj <"^—•O CO -•O
CD ni-v/^/»^» WtU*'*'UO*>*-•-* r""l/» rt !''*'-»V»g>O* gfo*in'TlLf»gjf*V«gfc rgo*'"-«">co-^gjgf r^cO'g
3 »>*-«grn»r»gJ/r'V^pgor*gr.Hr»o-»''^ingrco
O •*m rg -• gr gr h. o* ij»oorn r* groo —<cor**r\ t/»i*»rncD odo-oo g}-*r»r*^*m''» gjotrom^^^U^ODO^ *0*-^rwf»»rn>rO<~^ ,J0r>»
• ••*••••••••••#•••••3 ^O^^iAinoO^gJinf*- O-0-**»' rsiW0> Of*.
• -*r-gr l^r^^ 4H/*mcO-^^g'C3 -Of^mg^oO(J »««••#••••••# •
—*o*N -* ** rn »*» >0N -4 ~*o in g> >om ^ -^r* cm-^ -H rg r\j rn rn in >f\ C7* v* imr\
inr\jco»".r\j^-T-*>_^oo-^^m -*m'D f''-
CD •OrvfOcOmrO^r* ©-HO>©C0O'"»'rlC^ t*»CD T• inin"»<*r>c7, '*"0*> rr* rr
»rvo'r»'C -f^oor'N
rj «•••*••*•••.•••••.••
t»*CTk -0in fM |^O'0in'©OOCDC0^>0 *tr^rr>rf\
^* m^r^-^^'^>rr>-^0-^'^-^mvnin'nrMrNifrvm
<y 00-^-^*>J'M^-<*'s*'^-rMfsiOO'n rf>irMno-^^^ -^ r\j oj n^ rnin ino (7»
000*®0^c/'Nrof**ina)'^-«Nint>N^«
3 00-4«-»rs|r^mf*>^) 0OO f**f^OO'^t^r*O
**• f«ioo in compg -^ r*i <rom -o -o in r-twr»
3 0000-4*-*fNirg^^-r^cDrsJrO'-* ,wm-OroO
fsi(\»oo^'NJOMnr*o /»coiA-»- -ornocom*n Orgrnino-^OO rr**nmo T^(o^ino^',»
3 oooo —*•-•-*w^^ino^Om-OOf-rom
^O -O O f» h*OO <M CO—* «N (7» r» inf^ -* ^* tt>-*^)r»>r'*'0 0'»«,i'Tic>'Orrt<ricoin-r-rfnN
< o-^o ^mcofr»mm*nrTf-^^nmn^^
^3 tk»r>tnmQO r^'*--o>o-Ojpeocor^-^m
rn O^^ornrg or-o^nco^o-^o'N'r ^jrn^n^in
r*> eorgcoO'^inmcoi^i^^-ococ?, 's--0'Ni-^m C7* '*c^conlr-^cDc^'^^n»nf,|*m^moc7•<^ ooo f^O''»* wo-*-rtJ u >^>'^ ,*' ,^' r* ~rw<-* OOOOOOOO^HNl^n'TO^^H'OCO
pg rg o^mfs)N^o>0H'v®oot>O»^ C7» f»-.co K-Oin-0^oOOt^'* cOC7'rr>
<-g ooo^O"i^'Of*Hino«^n ^^ -J* co -r r*
3 OOOOOOOOOHH-4Nf^iiAK83(M^
gr •-• (^ i/»cOsfrgoo'-r", itr'C7*in',nn
3 000000000000^^-*N(n>liA«
>ooooooooooujmomomomomo1 o-^-^rgrg(Ting>gr»n
0> ocQC7»,f'^m-Tco'*»r— mr—OO •T<DO ,»n»r>j
• ••••#••••••••*••••
t» n»ft>*nm»**«or«»rnfT>rgcD«»—loo-u^^-ro•^-^rg<>io»PT>'Vtncpi^»r»i«»r-»^j
~h ^-«.g«^
in ^noo -rr*O"! o* co <0 m-^<DO C7» ro co co rgm -o -o W'O-^'—i**- *^i^<j»o -oo-u^coocoor"
3 f^^^g^ -O O00 h""0cor,w'*»inmn^rgop««0
CT"*>in-^-4co -* "M —«C7» <n^•r»pgi**rgr»-^O <nOx t/> rv< rgo fs-n *r rn co -O **»OO rslO rs< *T rg o
OfNmco-^ijrMnginr* oOin^OV^^^trr^m
-^-Hcoco(7*c7"s«a3mco-o^»o—*o-^ ,nco'0'*g
g>O h" r**C7»'*>'Omco-HCOCDO-*0 O^<tm-0u> t^» * rr> xvo i* cj n i v/* -v r» gr *n ^* ./* *^» gr ni «v
r* CT'o^'Oino-^NO'^'OoajnooHiA'^o
3 OO-^-^rgrggf^g) OO-^^COCT^OCOCO^O
^(*»0'V'>iH-ro>no^^taDN03*'AtO
r*h.mff>rr,cro p^-*'—•t*f*-0-ococ>o * OO»n »nmtj»y»m^*g*4> cDC7*C7»rou»inrrio-^tr-0-^
3 oooo-*~*cgrMmmtn-oo4>Og)'"-N»r,-mg>—i—f—«rjrM ^-g>
mo fM'vcovro-*'co^rNjorap*r*o^in^i^>C7tgr fvcj tr rio tr co <-• co -^oo co pgv in Vs »^f*
g/ gr g>f^gj^-«-^p»N«om -rr*^g^*'^•lnv»li^r>Jo,,
3 OOOOw
lAr^-tdfO^O-O g>rgjo>fMr»fV—tf»»U%—<i^lfl# OLfsu^cotf, '"*g'-Tt/*«-<a»cu'^v rn<;srg-co«>''g• rn rnrMgf gfcr»r*rg r>*C7'OOr"g(j»g* B^ion^N
u oooooo-*-^-^«xmm-ru-»*»wiggr-^m
u, ogj-^om^o^m^^rT'nf'-gjgjcy'gJ'vcrmgj(_» m gr^cr*CT>rn | gooc7»'>gO''*~*cDinoo<',,71,T»
rg r^rgiirt>vouou>-y«< 4»0"»rvon u »-^'^
ui • » • • • t • • • • • • f •
< Orn ,nrg4v csiN-0,'inC7'0,'romrg'^ ^rgh- om3 ocoooco'vt^r*<.g3mcomoo©OGOox Og>3 rg ^a—*-^^ j- ^•i-»r*rg--sj'^o—* t XJinco^O'^
-J 3 OOOOOOOOHH-^rgnn-rmMOf*)^
CD— u>mrnco^ J-> -H -J U-i'^'M O 1' to* -T '-o *" CO
wu;g,
'f i^'V*'Oi/,v, (/"4;'^U'*ii/, v*'»''*U
oooooooooooo^ ^rgrgmg^tn**
O O O O QO u > O *n o
^g rg rg m ro
35
5LU —
•
Zt3*-i/>O^ZU1Q. * UJ—X ZOujOO
m
• UJUJ• O 1
uj 3t-t- UJ
l/l <-• aa.UJh- -i<~—*UJ «UJ->-Z
^p-,^ z > <J^ — LJ-11BL B«t^ J£
ro ^ au>i
Qp ^-J-"U1 a'
<
u 1- •-•-xuJ Z^ «l-JQ. <«» 1
qj Zw ^•cwu(0
u• OUII• o^j^^o
• CJ
u 4->
Id
w OS
yACQ HwC Id
H >•HHM«c
Oa•H>iUid
t>
> «Mtr'm-rO'"V'TOO^
Cj w— —•— -* —«—t-*—-«
—. —.t,u-\—mo-« -o^n
0000-«<M ^**rsj-*OOOOOOOO-*^oooooooaoooooooooooo
| ••»••••••
*- ^nN-«ooooooOOOOOOOOOO o
O cocOeocorst^o-O-OCO —
«
^ pi uv f*. r* 'j* r« »o 'V* »
*• » • • oa. oooooooooo CJ
*rN*r>*nK> >r >r*n
r>* n- co .o*- »n*n eo -$•m *n •* #—•*o—»-^ -O fN*
O *M >f" OCO .TCOmO* T>—«C*U*C7***r'>r^O 0-*>fO rn*^mrr\-4C0.rC>:9CM*'*'0in0X-4OOC0 rr>C*
?> co P» •*"o **\ »rt -o i*l f— *n cotn •* 0* •*• <*> *»
>T -Ofrirvor»^rvoO>-HCO JO-^fnO'v»*"Otnm •H*rtr*inv7»'>*r»10 n*0*Otn<V\nin-*''-c*-*rTl^ fnf^i->«^-Htr\r«»(jX4ntN*"»r^c0J0>-^O^O'^ r^
Hino^^NN^sN(rNinift«foooo-4o o^--*c?»a>.*'^c*in ,n,*>r •r»n',»^fv**>H'*
^ »••••••#•%••#•••-•*•OO -••^'N* -**>^• 'T -O -O 0"C0 rs#r># h- J^> r^ (>4
i Ki li IfNiCM
i>_. O-* <0 COC^^OO ^0^*00*0^ -f^f^O"-CQ NOWlNiAH^dJHVJ'^^OOO'^'^COOt ** ^O^'O'T '(^ON"^ <» •T'*>fVO -O <*»T>V»»^
CJ #•«««••*••••••••••«OOO 0*-« —#<V r\»mm ** >* *0 -O O* co rs>—<m t f\
^•mcoCD^O-O'OO ^r\J-^T"si^»—«>0'r^cOC>m co >r >y^co-oiNiO oco**^ ^-o—-^ ot^O'W
•^ or* ^m -o^tcn-^** tf» ^nion corg -<of* ^rnmo^O^ninn^nf*! o O "> *^ *> *o r*
t ••••••••••••••t**ttor ooooo-*^^Nfsirnmt^'Ooa)©-«H
co-^mcornr*-^^} -r^o^^ ^i>(u^-*n
•V o^"iTflNQH of*fnmn'A r»oo*n'^^^
CT OOOOOO-H-^-^-^rsjnimr^vr^ -O O ^ d
* ••••••••••••••••••••CF 00000000-<-«-«HN'M'n'n^iA^^
r\j^ jjrniTifT> jjnjco(7»o pr»covrvmv»\no (o'f O^O r^<\»^r*T •t»r»c?'0-», 'OC7TorTnr*rN.cP»
v/ oooooooooooou-*-*^ 1^""*'
rsj o*»nrn^-injj^^mp*cm/> co ***> o*^-in r* ^-^ *r ^r^r^n>ro«fV'^0'n(t>-^',torg O00-^O r^*^'T> rV*'>-T',*',-'™*-^m vj-^-t T>t •••••••••••••••••«•#
CJ OOOOOOOOOOOOCK^'^H'^iMN
V3 O QOm-^COiMOmrf>cO r^ rr»<M-«^CO
o ooooooooooooooohh^-n
>© \r\ v r**rm*f •oor*o ,N'tT*'UM^ai*X ut CO ^irMtj VV*CM"*WWII >*^" -«W
o oooooooooooooooooooh
^oooooooooouj»now^oinowio>no
O* r>i-^r^»n-^^»^h»^ ©ojin rOfVr^fTioo,"^V*o* o^o^-t^^cooo-^^w^fn-^o^^No m'^4'•mm>t^•-o^^cr»^n^^>c>co^»^n^»^r -Oin
^cof^mco^o^iMO o ,K*^m^ f,">'0-^'<*co
l^ -* ^''l-^ QW'T aj^r^^r i^r»ir» co r«v^.^r^ ^
m r* .^ c^ co in *» -ro 'T^ '"* o* o» *»•**>")oo >nin -*'(i»3>f*>thrr»o f,»'^co-^<t>« ^-^«\ JJO*n-0(^ cocom f-|ivo T'**''*'« ,«Jcr'O r, t',,»m«v^T• ••••••••tt*« ••••••••
CJ *^-< CM rs»*nf*>m• -O -O O* CO fNir^t^ -OrrirNjOO
3 ••»••••*•»••••#••••--»-«-4_*rN|rj'r>rr,m ^. jj O^T'^'-^r.mN
CO r^-Hij'^HtnrnOOCT'r^C^ *>^»^» OH>-^©t(tl• 00°*'Tl fs» ''•**' * t^NOllUHN J'CP'O'Oa • #••••••
-* -^-^—* -^-* rs* r>i *nrn^ -r j> -OO CO <N| -4O in
rsltjrr^O^^^OinTO »OO i0^'*^'f»-f'flm f* r>-o ^ <n > O ^*^O /iNas^ ^ 0<~N*rg^O-n
«0(*>COOOO'MCO^>NO-T-^0',1JCO'*s|^'inC^ lN
r* r»f- va»*NJ'*>'s-'s*inin»n ^^**^«r\^»^c7»a>
fT)O prl <)COO>0*CDf*rM»VN-in<n ^rNirr>fT>-^r>4
O tfMnr-fSBt^cfw^xocMn-omvjcocjJjaocDO
O 00O0OOH^H^(MN(T)^^m^0i»0
n(>n -^*notn»nm^moocom-^co r^<x)co
»n ^^^inv-O'O'N* cooinf^»*n»^tf»-^inco
O OOOoOOOH-4-^HNNN'<>^'ttf>'0 -O
cD-t, r*-ocor\;corrta>rjc^^^^t)in*f'coc*>^cD>^pg rg^ «-« r* tn n> jjo <** *" «> -*> in r» co fVO r* fV
^ n»n-)fT>^^ix\'4>r*-crO'N-Tf,"0-»''^»incor-o
f<> -O—«0-^\mn'*V-^!BO^ c'* u^ t'^'s"C>-OrOCO
• m r^«Mr>*(v'*>m'rin»n'fc»coO-^'rin'7»'r>'0-^in
lj »n co4»^*r»i4j-^^r^.^O'-''m JJinrv^r.^'^-if*>
UJ • tat*«»*t««**«t*-J CJ OOOOOOOOOOOOOhhhh'MNN
2< rNj^r<trsf^-*^<Orr)'Ococo^m^incor<*r>jcoin3 ^^JDCOO^, rnfriOO-^^C>*C7, Cv—I 'X* J&m 0*
-J CJ ooooooooooooooo-*-—<^N
Qr— -*/<»r*<*-n/*-^LJ>u »-^r>ju>U'»* , MO'*i, i«;"in|*-• ^^ oouoo-^^-^H^^''ii>jsr"iinT^'«cjU> • •••••••••••f>«>»*««»Z CJ ooooooooooooooooooo-*
O ^ -. rg rg m rn T
36
o h-
*^ OUJ
O I mo
O-~0.UJO w
UJQ •
QC •-««rg
0> ^Q^O^^inun^-OO^rnrgrjirjiQyirorngr^ggj-g0> -0 o-f f^^oin^o-t gjg^^g?* ©<>h-co-*
**-m g> ur\ f*V* fM—«OO rJr-r- CO ~*r»—• rgm CO
tr* *n i^O*"go><j*<>gO'0<~grg<)<^»iVU*0 ,^<JCjcoco• »••••••••••«•••%••••
*n -rocom o* -o ct* cd to ft) in g> co g?o o>O **• *^IT> ajtfi ornii">rg-^rgtAr»rnu\mrg gfrg~*cO g**n
O OO-*0fN*^rnrgj-fnin grgjunoo^OO <©»*<>
•"•o-^un-ocorgo-^ogj-rg^gv g>-«Qr> t^mO r^^^o^OO -O t'^O-^^O^N'OW 0'^<"g
CI rgrAirnrN*rnrnmiAr»r*r>c»^ornrn-Ot/\cDco
w coco g> gr rn rngjm'~go uJ'«Jinrnr^rn grr^gv^in
to *"*OO 0***n rn •-*O»H *jm r»m^ co ^ r- r* y r»»nrnvoMn*ninmr»g> oa>'^HV4 -o^oco
-*—«—• •-• rgr* rt> r»> g> gf g> un r» r*- <© COOO rg —«
I
Q
u
co
% a. -* •«. a.
1 ac<
a. <*-* |
# uun
<w o<r y-TUUuvMQ
g* sy r\| r* rgf— tf> (j* rg ^-4 gr grm gr rg ,-#—i nO c©
m
mn m_j r*» u |—• » >* r» cj i/> lt* n »ct» r^ —• n >h rrj grm00-*0-^»-«"g—«rnrgrnrngr g>g?mf»g3cor»
—. ><-- t g*rgm-«O-«iAO'noi)C0g?'©rrvM
rgW^ * unCT* CO 4* rj^r<- in rnrgo*or-»r«» 4* uvj
f* -^r\j-T ^-fs-'N-—«Oin>rt-HO^in ^ rsj^ CD ©u-\
-* f<> «0 »*- CD <f\ >? -G •* t*VO ^O <^ IT* -*W CO -^-^
r- 0-^^rniT*-0 0**Cr''nrr)(s.fs.njrjcor*r^n^o*, Os
• #••••••*••«•••»#•••
0> P*O^»-0C7**0rgoO-riT»C0'NC0MT^-O',*i',-r^
CP ••••••••«••••••••«
3 0000-*^-*^^f\rvHNrslpnrn4'^^-4'iAiA
0000-*-«-<-i- ^rNjrNjrgrNjmfnvf-*'-*^
w-3
mH
•HUPw•HQ
OOOOOO^HNrOoooooooooooooooooooooooooooooo
(7» ** r*- co 5D -^ rg ynfVMO^-^o^-cofNico^*
0-^-^ |^J pn *rin'^coo-^ frnrN'Ocr»'-«^, w^GOO
in ^--4^ a>o>ocoir>co>o-<—«oOQiA
0-*^MM-^rr>*^invn*^-^-OW"^fn<J otr» V«(N
ooooooooooo--o-h-«-«^-*-*<-<j
o*1 rg <j rg ^^rg rg -y r>O u^m rg rsj t> r*m rn sf- <-*
O , ^ r>-ao'+)a>f>-r-c^—»mauo -*> -T^nM^n
corj»coO'>»^mrngvf*rgO"00"*»o rriin>t'^*o^^rsjgv^c^r^-^-^-orgin-^ino-^^m-ygr
»H r*»rng- imiAN^oonn -o© vo^^r^r*
CJ OOOOOOOO-M^-^^^^NNNNN
o
Mid
r* -^gr co <^» rgo* o^ g? w*
r>^m> -^in o* rn a? **s tr
r» -^*r\ *$ -^ co—| —< CD **
<-»r«mif—.*_#g»-co"ir»"g
^OO'n^OrNiOCD'^ XX gji-*wrn»' - !_* j <_>—• -^ -H> ooO^ncoinrgocD-O•~ -o^g* 'n^r>jrgrg_^-^Ck •••••••!•• U.OOOOOOOOOO o
r» o i-<fx>r* g>o^—*morf>^^orjTgo*g3r» -o ijo'^rninc* gr -rgr rfca^co-^fT^"
o ooooooooooooooo^o^w—
•
Ooo-^OHO^O^Hin^ona) g*i/» o-^
OOOOOOOOOC»C5 0<_»000000'-«
© *• * <H eoo—ifNitn-Omrg-J-»n gr ca g> f^ -- ^^romo"!^-©^'^ OOOOO-^O^OniO^OU^—•^rgr^nii^O OOOOOOOOOOOOOOOOOOOO
g>o^rmg>g>rgm *r-0'"grr\ t*. h i*- > rg -^ ,~*a"\—*—'n
rsi OOOOOHO-'O'MO^O ^OiAO O—*r^
C7 OOOOOOOOOOOOOOOOOOOO
gjmm g»- —( gjm f> o> g? rgin r» o rg—imm O" 4*rgrnorg-^rrl r*'r»inGO"itf» o^-i'ntO'»'nr*rgrgrgnmt g»gpinmr*r-(j»(/*—•r^grg*' gjr*v*o
000000000000-4-4HH^h^N
rn fC^r-o^fOcorgomirirjo^f*- ^norgrvj'n«»-oofgajocD-^' ,Jg*g'i/»a*grcofng'-^-t;-^•-«•*< rg rg rgrnm gf ir\m O <3 P*» cp 0"Q -^NH "T
oooooooo<->oooooo——|*^-^^^
gj rg com g> in g> r* ir> rnOom in^ - ^r^ h-
p
m iWl gjcorgg,o ro-^g>r-*^.^ao'om rvp«a3 g^
rg ^^-H—^r-^rgr-^mrn^g^u^m <u-v»,*Go^"r«o-^
<J ooooooooooowoooooo^*^
cDmONrno<n r^OrnOirtm-4(7,Ko®0-trg O"*—«—•—*-4rgfgf^>rn •» -}• tm^o-0N l)<D
O OOOOOOOOOOOOOOOOOOOO
g»oooN(DOfNta) —
«
r*c«jniujii»<>rfCJujr-« <.
» • Joooooooooo o
<;mg^rg««»m'*"m»^g3—- .
"
', w \ uj — y l u- -r (.i^ j-
-^ ooooooyoo-«o-»oHoi>io^unO OOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOO
oooooooooo••••#•«*
o o o o
,-h —t rj rg rr, m g-
37
z ~—u >-
O • i/>0Q. —Q.
O J'Q.aio ~-
'JJO •
• Q <UJO*-y- uj
to <». ote *5£21U— _/<« —UJ 'lazX •> o4 «o-^<at Ot «* * 1
i^ < ao>a.
1 act<N i* -— ULU
_j Z.e*»_l1 a " < 1
Q Z •->-**«/iw_iiJ<:zu3
0)
(0
• UUII• ijOt/>i/i
U
fN wt c
O. o .> fN-J/lHLT«>«k/MJ*O r-'-"*
1 -* CM*1 -f—O« -O lTVf»
•H u. .0<N r'J-«-«OOOOOW 4->
UJU
hJ 3 uca -Q«fl •HH M
0-*'rt'0r03>a>o®mID OOOO'^'V'AHff'flO
M 1 OOOOOOOhjHX oooooooooo
•H 5oooooooooo
Qrr>—i •-•m -rv tr*f» <o o
+J» -*^Ofnn(MninO'Ti
\n ror*-r\jr*-ao.o*»f\im^0) o ^^rsj^m^rn t^QM 1
00-*-«r><r'1«">^0> <«>
«J «/> ~4
Oi
X • ••••••#••
w ^rg^HOOOOOOa • *oooooooooo
ut•^ -J
O r^o^JOO-O-OrN/rgrg *«. «y ~>— -r *r "lo*"*1^ p—
P- *f^-*-*O000O0 <** • • • • 3CL OOOOOOOOOO o
O* Of^-^^-O-*'OO<T'O'*-4'rMJ-»rfMnN0-^'^rna* *>*^>*r^*^mo-«^t,
's*'*>3><o-*ir*^ (N'y>-*ot •••••••••!••••«•••••
07 r>J-^rfV>i»A^a>f^^HOf*»nr*>r*%r*>f>iu>rt^rt>^
f*» Co «^—I -*rt>0*A *> 0* (*)0* <0 Ni**>0* —« *A (X> fVj
• ••»*•••*••*•••§*•••
rg >r o*a t>a? <vrg ino a> -o -ro*^—• •« *• -o *o»A COCP»rgcor»4n<jxcg.© CNO^C^lJO^*^
NO -00*00 •©'*>«>Ox o*r<».^.*.ocg*»i50*"<>«o gr -*> ^m oco^^o^-T^n # o^*-u"\f*)<?>>r• m-ro'>oiO'0-r<^ f,*-oir> tO'Ti^'n-^oo ,D
af ••%• •• •
OO-*0 -*—• «^*^*f% •*»»tma (O CD -*-^ vn *noO
m -^-^-or>go^tr»'*icD'^^rO'r»0'OOiA rr>r»t»nP* <# 4>coa0 ^rr^^^—irg^jco*— •^^'*»r» fvOf>5»
CT oooo^-»NNnm*t',»07i (>nfnh.r*
CT OOOO'^-W (mim-*- tO'CaxD^HintA
« -tr^^in^y*n*OHOHtfl* ?o<i^i3
»nor>J-^'* (I>*A-0'^-^-^<X)CT'C0tJ0d>a>rvor*-tn ON"iT>0'Oi/soino'N rr»N'*' |0<Dmtn'fl^
fNj >» ^o •* * ooo e* ^ *» -^ ao -^a> rgm fsimlT\ r—O f*O "1CO rsrf 00 OO *T\ H> -O sT r» f~gO **} "H
g> O*^«^^'*>if>^^»O-«'«>r*rntnf^*i»<»(0rgvt ••••••••••••••••••••O OOOOOOOO^H-^HN^omt -t « O
c» oooooooooo*->^*^-^«**>*''»pn'*''e
W> ^0*N-fOa)NO'V^tnN 0^'0m co n^coo * «^cir\o*-v» g'o*^ ooaorg*>* OOO-^'^'^'^-T •* ^Jf*(7"^*'f*»0',lf,»'V-• ••••••••••••••«t««t*
(j OOOOOOOOOOOOHHHf^r^Nmn
P«* nNO<l't>t OOTMaoO'^JOi'^ -to»MOO c* ^rgin-ro-< r^'0>/>rgu-\^t^w^
<N OOO-^Or^-^^n^Au^^tO-^rgi^N-O ^ CO
C7 OOOGOOOOOOOOO-«-t^^N^^
~-« fT) »r f»icou»'4>rsi',,»o>y aO't —««^ tOf •*/ O *"X fti'Of ninxn 'T'^'^^/
«-< ooooo^o^oN-^fi^in rr» -oi/»o>rn
O" 0000000000000000000-^
a» r^^^^in 0'<>'^oac»o*rvtnco ,N'*,*iAooiAa> *• •* -o ooo tooN-o^o io**i4>m**)<0<+th
ff> afi> -OO> «!•* <NOW1m rf> ">m f*»h" O 0* ^«rn
Lf *^-^-^*HO*-v>auo'J,, t/»'T> rvr^fn* toi*'N• ••••••«••••••••••••O ^ojniyi-f *«'OU 17"r -4*OOV*oo^i>«vrfl'N
r>4 -T 0* O* °**rv -^ ^3 r«» t* r>« -o cgrn O*in 0*AO ^/>
• *••#•••••••••••••••
p* -^o^ f*noo <-<o -^o rn*> </* p* -o*^o o*>
9 •••••••••• ••
^^p* h* -^mO "I r>JO *Nm rf> k. rs#mo >»" 00 -^ 4*
CO n» o^aJO-H-JO'AOOrnHltirv^N'Hinoi'H
O t •#*•••••OO—•—»—»—i^irsjvT ^irnnaoao—«-^u-iu"v-*—
«
*A sT>tOOO fTl-*'*>-<^0,"X>>r 0D»> >"0«>*'*lp*. f^r^^—. o o r tmmoo^^cr'O a *<*><**
(j oo^H-^HfMN'tmTiiAKNff'O'nf'KO'o
AiO^JJO^AOt ^H*ff)n»«ONin^OtP^ «OCM>-f^OOOOT ^fnTl^^-OP^TOO
O 0000-^-iNNff>'n>rt'0«a)JDH^ifiO
^^tr^O^^O O-o-frgooofM^rgo^-^rao
O gr ^^-r»oO'JMAn»rtinv>fT>r*Cjor-. o^CTW»rg
O 0000-^-^«-«'^P^<N'rt'f>^4> O-OOOCD-Hrg
W3 4>*\imO»'M rV*— 01>0**»aDO •ON-H'nO oP*« r*. in tA COrNJO^OfMVAO-t ^O^iA-rO** ©m rr)fn»A*r\r*co*H'^',*r*ir»tjn«»©O^Or>»r-0(g
o oooooo»4HH-4NN'r>m4iA'0'0 (y, c*
N*lAf»P— r^^>\AO**r *0 0*P*-Om^0^*0^*00P*-r*OO r*o»AcoiALriAf»-^o Trg©r«-r-^r\j
•C Airg^ jtfiy'Uijrg-jr-w^^ © r* 4/ 0* *» OJ
O OOOOOOOO^H^H^fVfi^'rt«J4
^Ps|©^0,*r*)f*>-*\Ain''-OU"»0*'fN|P*oxO J"*• i>troOa>v*'\J^-rgoo ^^^t_»oJO(/'«^^-u»'4j* m r-»^fN*rgT>>fvA©«00>» r>J rr>coaoiAiA>r ^>Q^
u ooooooooo^>^-*-^-««',* r>"T» fn'C*'
IL -^lAP*0*'0*'-^C0-^4> OO^-'*''rt0DiA<sJ0> ^0©CJ lA lAtAfvrsirg^g-o^'^iauiAr^r^int/'OC^-T-T
CM -^•-*f^rMnipn4*u>^0p».0*O ,', *At/»OP»r-»r*T0Ui t •»»*«tt«**«tt**»t«l|-i O OOOOOOOOOOO-^^HHiMNNnmp"
z< 0*0 ©coo^A©o*»^" oooNN^m-^^O'^3 i-Hf\i»^-fs-trv©iAco^^O'O r^™*X'^ r^rnr«.roaoO rg •^-*-^"*rgrgro rrtiAiA^-CO-^—<iA OO-^00'>
-J O OOOOOOOOOOOO-^M-^MrwNN
-^ nr*. —« ^ -ijLp.—t T,fv'^—*" ci uj o *<• tJu-^-O'-wp— uimww^N >o <*»«*> •«•*" «a*t>ju\o<»« , ' ,* r*tJ
O • •••••§#••#•••••#••Z O 00000000000000000-^-4-^
X o—^rgrMmrngr-riA
o 1T> o• t
IM INJ n
o o o o
I O -c h rj N
38
5^
QW-a<
nI
Q0)
w
u
3
W•HQO
0>
U«d
-
t/*-*-;wi O»-l-4tOO i^»-^
~*(J-o— a. •
%-*—r-o—uuoa to«r^»-a. uj
. S• a.
* Ui* O I
UJD •
h-k- IU*/» «— oae 0CZUJ3aj o»->-
_»« « —
i
Ui ««.a^A > Jm. -*t_»-j^=L CI •»•*! ».^ ocu->U. «_<~l_»
I ar«»•— --etaJ -I ^. «5 -1
Cfc «< 1
s *->-«:i— "l^>UO•^iU J
* our x• uu^o
3 —•0<"VJ-*fWV* r*><N|rf>f*>,*rt> lft,#-trnA'©t/\r»-0
rt1U"\m *VO ^"Hl * "^ "** W* CT» eg 0»1> r^
C3 OO-^O—rg— eg <%j ,«><•*mfSK^r^^r^ -*-*
m fgo t*J^-*cr*-«r-'^o<"rvr'"^-x-*cv'>j,rO''*i*>» —•rg r'"»r0^U*>C0'-»O><"V-*-* ,
"r*0U-» ,30*»OO
o »vr^ rsi •>mo its -o-o—<o<7»-g^.o -o-r **-—
rgrgrgrnUT"r> O -T '"•^0=0 00^0 fNO^I^O
ty oooooooo"<0' oooooo-
•^ o — —-- -j -\> -n ,* «^r\to oooooooooot oooooooooox oooooooooo2 oooooooooo>
^ <^ <"g j"t)'*»'^*-otnuj r^O-J'ls—• -*n *> **> ff* .ft
I • •
>- OOOOO—"---1/1
a^ -— ,_ — vijt-^ -^ ^j
ooooooo—<H
* OOr^* O «MO -D r*
*0 0*^m^<wo T3 -O
OOOOOOOOOO
1^ C7- -« -fl O* «1 <"g—*O »* ^* k- CI "• «V #O -^* -^
^» 0-^ r>*'r»^^0 0<oa3OJ»'N-* rr)i"r>invnr**,o
O OOOOOOOOOO—O-^-*—^-^-^^-^ o oooooo-
'n^t>o^ N*<D-o-*-oO'*'^*'7, '0>r(ri-o ^o
ooooooooooooooo- o oooooooooo-
ct oooooooooooooooooooo
r* %ro^^tocoo*r\*rrsjfvj^>.o-o-o-r'^—
<
C7 oooooooooooooooooooo
*_^ oooouoouoooouououooo
m ^ <*> O 0* <C03'7»fM(>^— O'N* « rg <? v r~>« i^-o—**^ -W-O
00O00—^0'-*0'—O^O""*— rr>—«'', >'"*'*'
oooooooooooooooooooo
m >f iTs -* lT> m -OiTt^i-nO —<~gm -O CT- ^J irt 3J ^O-t^iJ*-^ooooaoo-,o-*o^ONO nJONO ,,i
oooooooooooooooooooo
C7 oooooooooooooooo——I—•—
l
oooooooooooooooooooo
o ooaooooooo*-*c3<-»ooo<->oou
UJ • ••§ ttatvtt**!-i o oooooooooooooooooooo
OO r^ rv^r^l/^<t)'Tl-^-^^/^•^3D•^-—«o -r^'^^-
o oooooooooooooooooooo
** •••• ^a. oooooooooo o
— ooooocjooooooo—o—o—o—3 oooooooooooooooooooo
ooo o<->ooo -*—-*—•-"— -^ -*-*—-* -*
oooooooooooooooooooo
o o o O '
OH-4NNm(Ti>f O -n ^ rg (NJ m rr>
39
o <o •^ Vo <a o •co »H "» o
• •
1*1 o o -i
o ~+ 09 \t\
o ""» fM UJOJ <M <N O• • • *
fNJ O o ^
o o » <N<-> <•» <*l *~»
o m i»* mp o n in>J> rr) pr» _• • • •
«M O O -*
o <r» h» 1TN
o IA O mN m *• ~-*
O *• •-• f*l
o -< o> 71
OinO^O*JJ^N-<>ino>-< o -* -I* -H> ^-.MnJUO-nlOfM^-fOnCO • • • •
I -OO ""• <M ~t —< -M -T J^ rr> 4> —1O 7> *» IN* O O «H
*"* O ...... ft. ...... ON.-0 33U* |.|i>|.-*»*.«*«-^^»^—ip4»4i^p4H ui u^ v/^ n
[J Ol > ifl N• • •
„ - -< o o -•
0000—•-— rvj rvj-r^^ ojo^h©OOOOOOOOOOO—«-<-N/tN| OOOOOOOOOOOOOOOO o
t- U x <_>oooooo<-"->o«_»i_>ooo -o *n r» n• — • • • •• ....
rj -w* QC OOOOOOOOOOOOOOO -* O O iH
:>
H _* O *•. -o <u
J M *"* (^iTi 0"^OfNjxl">-OOl>r\j m>f\J -o o coL^ ," > O^O' fnrirMO B'M"10N>»«1 ->/ -0 0"> r"(
CM jjp- tu noi^f'iJ'i'iOrg/io^iAS.o ....,3; Iq l_J n^o«i-iO"100-,rV»'0'\'\ «* O O "«
*"* _, t-
(0 • •
• »•••*•••*«••. • o c
— —- —- ur»-i«f-»™<*>"tJJ'Ov«(AJ O 'V **• >>*
OQ.O 1oxo X«UJ »-^»— —IQ.O XO UJ. w a
-< a.
• atII » -< 3_/ iu a:
# < t- 1—« > <— a oc.
a J —
•
«» Of «* -Jf— ** A. ^ •
1 > a xo_j->—<<l t—
1 1 cc r ~-t——— X a.
3C^1-JQ. 1<t 1
?H»- -i ii >-»'"U'J LU
*-<. J_» -J• cj r 1 1
• UUVIl/l X
OOOOOOHHrfiNlMlMI'l* ~*
so r« -r -r~ O s»- -^
•* ~Q <^ 00nrg^ni3)^000 >T
O
rNJ ^* -^i7* ** . . #
I'oKunnu^v^flM'lD'^'xair. ^ o ^^ >>*
H)OCOtT"-— '0»J^ir>00'IO ,J' ^o
to o j-i *"*i n r>jn —« —•—'o o o o o
I....... ....... • O u'i CO
OOOOOOOOOOOOOOO •*••x . . .
h* O -* •*
i °— OOOOOOOOOOOOOOO
ui-or\jtMO uJ |^"STH/s uwv-*'\i r, »>0
OOOOOOOOOOOOOOO
OOOOOOOOOOOOOOO v/ UJ -» — X^K
OOOO —* ^H •-* -^ ^-» rsj rg rg rsj rsj rn
40
w
o»«**rt *of» <orn»» Of*o» o>m ^n <oo»n m-om »n^fn inm« mo** -**»<o -m^N m-oo -o*r\-*O f**tf%» o^fx «©o'*> «uoo* o<o rJ ^ojrr) o- _• <x> <v-*o -#rjf>j ornr*» r»mo "^ohj m-^—* mN*4 >rco<oo -o o -/ nno oo-o 'O'*^ «n*r-^ mr*>o ^^o o-c*> oor» a».©i*> ©mf*i o*»m <d^n -•m oooO —I.^O r>#f>*-* "H*V-< f*»mf* *-*-«) .»r*w-v,r -O-0«"> f-f**.<) «9»N 009* mrs|-^ tf>*-rn N»r»^ —OO ">^,|N
<r*»r># <vmr>t +*-o *>»*»o oorsj a> ^ w-»oo mo^O ^O"* <rout o—itnf*>*«^ mmr~**m <*> j- -.« ^m""** itfOIWl f«|/t^ nif*-" i^om UO*J 00 1** ^»ooo eve*** o<x>4 *^'^ "*oo* •©•"••hj ^r*r*r 1*11*1*1 m^r**! -oom •-*<7«(^ » o -©
O p^» «o »« *o «^*^ m»f^ w*»i>* *-*-<-n •nm-c -o-<7*> *f *i o»cof"> oot
*^*-^<o ^*%« <erM«n 'O'*o o*r* o.^m «-rw <yiv»4 w^* moo> *e#n»n r-»o»*> o»^ worn ^inp*^ rx—»-^ m-f o mrmm-O fMO*-* f"»r>4iTt +rw 0"00 «JOO -©-*<">* m-OU> ONm r»o*>< -^,^,^- wr v *j rf>*f*\O pwai f>»*>*« r»*»»0 i>*"^*M r—»-"0 m <*><</ O'O'M r»»»«^ */r»o «U*»0 OO^n -C*« *T-*»n -**-^»n otnO
o ooo ' »o -*-*•* «^o< * wmn fnmoi *><#•»*» <#**-# mmm oo-o »«>»» oo« —-*o w^m«N gw»^
o^m >oo**> "^^tg o^m o»n^ *»-<-si-o ***'»* o-ors* Of*vM ^w\«> Nf»* omm mo^ f>«o«> -o^**O f^O-*" Wh—N lAw^-• -O^r-O O"- O -Q sT***—• OO-*' *rw»«A OO-O •-•OO |>»*^tf\ mO<D ^^rsio **»m»A ID-O®* "i-^>« f-^-»»#> ——*uj m*>*^ v^l^w-v *" -^O 00*W» • »«*•-« rvr-v^U ——•<) UOO ^r*«"» «-.«->-• —o« 0«*»*T9 • • * ••• • • • •«• *•••« ••« » • • • * f • • ••• ••• •
OOO OOO -* *0 «** —•-*—«NMN mr*c>4 mtr\t+* * *rn tntrt^ *-©*n p*f»^j »cd« OOO* r>M-t«4
O 'SA^ 0*-#i>| r>4*0+ (**^-*«%rsr^ #mK ^O**^ "*00O r^^^f^ rs»m<N nO><^ ^m-O *^0-n h»o*»n9 **» (M^>\TS -^O'* Nt>»^ OOO* -T-^O ^rsir* (^>00 TO'OC^ ^%r»'» r^rstvn o—'*T -- * -O «0>A ''•ajr^• OO"* f^rM^ -0<0<f> 0*<O(D <M**»iO ir*»r»^ ooi*» ^H*^«N ©coc * -*fX «**^^> 7>o»» <D(x> o oj^^» p^ «qO • •• ••• •• •• •••
OOO OOO OOO OOO **-«i «i t m -*-»-^ cvtnmM Olf>*oj mmm <*+ r*\ ^-r^- muMA ^<o<o »»oo
^ <x>fNj^ ^>ryf*t Ok«^ -^©O-t-^-^ ^*o-< vtoo N.o*rt -+\f\r*\ f+*v\>{ »vm ^ f»>^o is,»w\in r\j<nNm *f r*-^o *tn<^ -<®o r*m«» \nu%-^ oo*^ a>oo ^-^*^ ^o'X ^>oo cr*a>« »-*a>aj oo-m oo-J^ OO^ . «.*<->•> J- j- * ^-^f*. c^ r» •jv rs, rv*-Nj OtTttn ^CT»d) •"T-*'^ 0*CT*W •^-^^ »^. <Q t^OCD V«9(B <ao^
O OOO OOO OOO OOO OOO i. i i « i i i jp< r^v^J fs#*>|r>j mm'n ^«r *• ** *>MMA <»^-0
f<» O^O —»-0« *\yOV* C^tDO ^*rvj^ 0-0t7» (DO CD <T*m<* f*>®-* 0**^0 0*>*"» fVt^l» -O >O IHaj^(1) "» <o«">4J -*r»»« -*— 'j vtOMiyoMt ( »-«<^ ^/ # <- um«-^ ^»>o«» *'»/«i —a>«C -ch-nt m^itn r^f^^j
pj »a h. ooh oo*n m«^-r iom-o '•'•»ooo mm'n <><?<» ooo v\-** oco> ^o»ntA rsirvr>i ooo ooo* "* 9 OOO OOO OOO OOO Ooo — i— •* w+m+*4 m*m+m4 rv>«f>j r\»ojN tt>estr* mmm *r * s ir\miA ^-o-o
n» ^ mmiO «^-o»*l »•«» >^rr»r^ r*>irt(N
O O ^-rr* u^-r « v^i-mou.o OT>-^OOO OO^ OOf*! rv*^* -^ -«• -*j o o x> <S*<x>0
w(JCQ tO ooo ooo ooo ooo ooo ooo oo-
•H^ «r\ ^ m^»-— oeoO cv^»>^ -*oo ^^O isttnrg p*-^-^ ^«n a>a><"*j n^o nan p^*--o•• m -r o«mt\ sTP'^ocO cdit»o f— ir»^ ou-o ^>^-^ o-TO ^ro-^ ^O-T r^-oo orvnA
^J *l OOO OO-^ 00*x OO*^ r^^*' ^•^o io\r»f^» p*i^»o OO—• «>#r** - »ntr»r» irtgo »*>r<>«# a>r*-o mm-*"
C3 3 OOO OOO OOO OOO OOO OOO OOO OOO **0-H **—»-^ ' ' « -^^<M fMfs»r>i rsirsjca fnrnm
-^j * -r fsi a> m <Ofofr>»* -ro-r w^rn^ tf\-*»^ »>mo o^^r *v^-»n no« -*om OO'*V^" «n -* 9 »n O -c aof»»-r rsri^^i m»*nr «r—*»n *ro^ mmio ir\oo «i/,w« a? -r -r «>o<C
ooo oo—* OO-h oo^ 00"» ^c mr*m ^r * <; -v-o x» woo oor^ 'T>r^«» <o«p* oo*4 rnf*>«n
a ooo ooo ooo ooo oooooo ooo ooo ooo oo-«
A O * O *^ r*\ rs4 r*\ir\*r m^O 0\*® -Om -O N*< «^^ O^-O ->>#'^> lf%f\*«fn 9 <"X «3 ** o "^ ^^ rN* <j aa *(^i^ f^mr^ ^•%/"^" mmwt motn */*•**/* «»iy^*
•^ OOO OOO O^J-^ OO-^ OOr* oO"> -^o^ *V—»-r MNfl -#-*r* ^>m» WHO OON r^f^'T nmNl» ooo oou ooo <-»oo oooooo ooo o^>o oo*j o^o ooo <-»o^-* -*-*•* -*-*-• -*-*—
*«* O * e-4 -o misa>8) «\-*^ ors/rsj rsi<x>4> (Nnrt^o *\.^»«» f*r»m fMfsjr- *ir»-r
tf\ fn ^ o •* 0^_m-*»^ ^*-*-on rM^ao moo moo OO-*" o>**>«^ NOD tDr—rr\rx OOO poo OO*^ OO** OO'^OO'M OO*^ ^^om *>*-** mr^«r» ^^r^ viinm h-*^»o vo»*N «-»-*•<
X O OOO OOO OOO OOO OOO OOO OOO OOO OOO ooo ooo OOO oo-* OO-* •*—-
•
•+ o o* f*> mm \r\ •tt fr» w -^o»Ht' «>^\-^ ^rrt^to (Do** m»-© o—-o fsif^^ii rsj »A ^» »< mo O O O-^^" o-^»Ti O*^^ 0-*"\A (NfOCO O-^*^ r»-fT>-^
S r<i OOO OOO OOO OCH OO-* OO-< OON OO^O -^O'*) ****-*+ rnrMin mm-o in>r^* h*^)0 «<o-^
O OOO OOO ooo ooo oooooo OOO OOO OOO OOO OOO OO© OOO ooo o©-*111
w4
^ mm t^ *% *\ ^* *T -m >r r» —• (^»'<-*•^nlr•«t»0'^'C^' ,*
< m4 OOO OOO OOO OOO OOOOOO OO-* OO-* OO— OO*^* OO'X 00"1 —O^ *+*m)<r rwxrt
o o ooo ooo ooo ooo oooooo OOO OOO OOO OOO ooo ooo OOO ooo ooo
41
o CM en mo O o> oot
<* o•o
en O o ~4
o rM en n»o -4 ^* oo3 •-• -^ o• t • t
'> o o »H
O o CO -ft
<J "1 ••1 •-«
-o —
a
^ o• t • •
CM o o -*
O <o <o r»
? o o f4—4 -* o
o <r> •* o*O' O O rtN H N Ot t • I
<N O O >H
O -* O cm
O «* m en
>0OCMf—c©Oc— CMeo-JcnmN.cn-H OCMcMO>0>j'.^co«0-*Ocn"0-fmr»cn'©eM • • • •
I <7«a}.o<ooo(^inu"\com>», fMr,"»cj» cm O o ^HJCM0cncM-*a-(O0000OOO0Q ........ ...ft ft. .^, , N _ _a ,* -ft —I —a -a -a -a -H .- —a _ ^
in
10
U-,
w «^-J X
< *£Eh
T3a«3
"x
*
•«» CM «> V uy C) m >M r» r* »*• U» r» w «sr mj O o o H CM en in r» -H o -r in •r TM O
1 o o o o O O o O —< -* CM en m CO <NX o o o o o O o o o O O o o o —
<
a.
<
CJ cj o <_» o CJ o o o o O a o O CJ
o o o o O O o o o o o o o o O>
•-. r\J —
1
CO o •0 m tn CO IA 0< ~4 e'- CM CO <M> ^ en * m >! CO •-4 o CM p» m en O Cf CDUJ m •*• •o m C7> CM —
-
o •o m CM m -0 *t -OO •0 o •T •* —t r- r- CO CM 'U it- r- •r p. r-
1 -r ft^ o CM in 00 CM r» en O ch o «n o r>-
o •o o -ru v/* o TCO CM en o
ft t • ft
~* O o H
o CO CO C*O in n» in
o en en o
o m o <o —a * •Ve- -* o r» r« ** IJ>
in .* —1 <7* O en 0o o o* m m a-4 aCM o eo vi CM CO i>"
•4 O O m4
O il\ O -T
o m *~ co-t -r ^ o• • • »
^ O O <H
»/»OOO'^»H-HeMeMcn«ar>*'inr»0»O O H N rg-H O C| t7> cm
^ in m h• • t •tVICQ^NON«»o>rr-or>--ocooo-isin^iijoj
I—ir(-^co^a:rgT-OOC^mm--o OOCMcnxrj-r-oc7>cn-o~ft'4(eMOcov>e^cc"- o<n<oco• >•••••••••••»• o -0 c~ ^4
_, -. -oooO'^«-«cMeMen>»- ^-m»-cx>0 «»••5 S M ° ° "•
1/7 l/»
toi/) r»w»coO'^-^ ,Mcnin'^mo>co-or~ o^^m>v>-a"^ Nr-<r— coa-«^;>8rnii/iV'»^o<Mr<»>*' cjo-^oi14 u. <X —
*rl
l l-'" UJ \J UJ (>J 'M nT" -+ ** -r «» ^ ^/ • • t ••v.^'w (DiM»r 1oo>cn'0'-»'OeMOv/, i'> eMo,>r» • o o »hi »hOQ.O I #•» *>oxo XOOOO^rHeMfMfn«r«rme<-coo• uj > -» —i o m ni o—•—-m -» o r- en oo xT x -o cr> -r -r
O uj pj n) ? o -f M -«i->0 cm cm co en cm O co ~» • • • .• w j n pi' ^^ v» pi r* co n» ni in cm cm u» p* ^ ^f o o »h a-t
cMO cXOC7>^^moOOr-cocMcomcncM /*o r~>roocnrj.-o*reM-«-Hoooo. lU0-*"encM-^OOOO0OOOO0 »or-mo
II n -* 3. >.l — O en vj -0
J U) o;000000000000000 X'teM'MCO#<l— p (_,...• >< ^.O-^CM^« It CX ttl
C£(J — OOOOOOOOOOOCJOOO >,«j x *J —' oe~'< ,^e>-^r»ujcJCji/, -»
, 0'-<''^ -^ociowr-qis n yuivr»^»-ii>ft, '4^ujur^uj»>*aj^>ari>* Oh^'-uO< >0 X<U-T, OOflCUin«J"CM'^'HOCJOO CMUlf."*cj_i_j—i«» i— -o>rene>j^cjoooooosjejo • • » •
I I OCX —•»•••• ..•••«•• -o^-Ten(--t-ct 0.000000000000000 —JZ1L*X-1 Xa <! <j | — —~ululUO LLIOOOOOOtPOOOOOOOO ^'uj — — Xi-CUO JtM^T'OcoOIM^-iVcooeM^T-WcOO -IXUJ —OOXX I ............... ft I «• >, 4ftOU^m XOOOOft-tft^ft^r^a-aJrJtMCMlMCMin •X^<£
v-<>o
42
0)
fN w• to
&H
w —JCQ w< 0)
H H•HP=id
Sd
-** O 0**1 IT»©*«> h»dD -C **-0.^ O-O O^* OO"* *t>f»>0 WOO ^^^ -*0> o -Q a>—
*
»— -O O'*o ^no (^ c+rf> W"*-»«-« *. w>m fN^ r*^>r- *coo rw-r» r*mm o-o *> w>o»f>< ff\r»v>r "#-*o o -rao o**oc* wr^cfc -* <~*o «*mr*j v -on wkdo <«•>*'• ****>« «©»n.-^ -»*o *»-*»••> «o*<n n o -r od"-**i as—r^n o*>*nt • • • ••• » • • • • • ••• * • • «•* • • • • » » ••• * • • i • • ••• ••• •••
CT r*r*0 «* «nc>| -*^-<*> VMH# O-OO «»N 00-> NrsfN K\in«> •&«» **r*r4 »—**•*. rwyi f*-*0 -*> O—-* -*_—
4
. 4. 1 M fc I r«ofr>l WNrf* «W»y*> -r -T * o-r -*»
w>f»o* -oon *«o o*v* *>*>—« ***f4 o*»«© nvno «oa»o f^fn^ 90'*' •-•?«> ^-^n *-o^ ooo9 ^r— r-W i> ^^^ ^jci rry^-in Vlhn •»»f\0 **U»l* VV«V tt»«f« ntr^Hf V" 1*"'! r > -O J -miv • »*F^» ot>^V* p— oo «r> ^r^. v>o<^- o««» nhh '•*—t<u •c*».^i v«r*f*i «cy> ovo **«n*^ t^-^em no**i **g*-4> —»f*»a»t • • ••* • • « ••* • t ••• t • « ••• ••• ••• • • • ••• • • •»• •••
fc» l' "O •>* r*^ t^nn» o-^-tM nmn »—r»o «ow ooo r#ci>f>t: w>*n Oc*f mmm ws« wr<e (*vr4<4« i^ mm~+>* wmm+m4 »* *-^ c*f>ioi n>r^i !»>••>#•> **•«
rv-*^* *><Mi *4«o ^-«>—
I
i<oq ooo Of*w* "rwj'n r-aj-n f-«%*i r*ontf oo-*> «-\o—
«
o-nn r**>*-%•ft 00*>*) 8D — t-* ONO avrvtf^ Wifl ^f«wn *0*» tr\-^ri| mcoas OOO r»wm o** m no11* n#^ro ^-r^
a "'O -*-*-* r^r^s nvn** <*«*> »\«\»n OOO *&«n. Q»0^ »>*r>*-« * * -» H>t^»* i i I O-O-Q PMH
r%**-< w> 9^. -*^.^ -^r^aj r^^o «r<v« * -*^ »-<T>«) N*0 <0-«0 rsK?r>4 V>9fn mVMO k^^ *-o ^^ «^ao ^r «-—
i
o—«o r-oo ^^m>* i-yr>KO ooo »*-*/» w-r's ^•^^#*>l r>r»«© f-oN -*t^ o*ct> r+r*)W\• i*"-*^^ »n f^o t^o-o w>«i<n 'v^^o ' * «qp o—«(^ *^^*o irv-ow^ 0*^0* ««-«>o« vr*r« -uro-o <9«nm ittW* «9 • • • ••« ••• • • « • ••• ••• I • • • « ••• • • • • t • • • • ••• •••
000 -*-*-4 *•*• 1 r^r^r^ mfn« -r*^» «vn> >o-o-o m » » ^»» > 1 < "Vn^ 4^4 000 ^^^^•OD 4> o~4 m^m <T>~0m «W .. I <t.0(X> OOfl ^*^fM lVo4 0*»*t «%^f^ O >*M OOtNlO «0> DON
00 i>#om o—m noN o^o«oo o—•—
<
o—-^ c^-^i>j c>-* -o wcmo ir>f*--r w»—* a»o9 «>**»^» m^-co ^»—
m
• (*>r^rn Q> ^^, rv^-^ >0 Jj-O rv^*—
«
f-»07^» -* tT« * <~+rryrj rvVN «* 00<B 0*%«n ^("•'O r>*»*>-^ r-^ -r r^
7 • • * • • • • « ••• ••• •«• • • • • • * ••• ••• • • t ••• . • ••• • • •OOO 000 * ii 1 "*^«* r«>#r<4 **r««>J f*lmm +•-+•* nvWN -C-o-O w^-»w 9>9>0^ -^.^^ ^ # ^ «n^*p«
r^-^—
(
Oovy rs*^»^» c^^ « --^oo <r»*\-^ «-.-*.-< »«< O*^ tn-^—
1
aomo »MO*S -^vsr^ «n >r « 40>tl*> o*«oct» «^ p*ml rrv^- ^j o— -o f*-r*.«^ t^»c»-r p-t7»«^ f»-^»» rN*^r>4 o^nn m«"icci m^4 r>#<y*M^ r>»>-^ o#a><#— _-_*^j ^> ^j^j OOO *-4>*n O0HO09 f^*n»n 000 O^--? «*>« tnw>v^ a»a»r^ *n*>*rij mqO rvnr^ aooxo
O 000 o 00 -*-^o »< * » « <>*tn^^ *<*is#^# i*wnm <<#•# m*r\«n o-o-o «>«>« qqq nnn -#-#
**^**i rg «^H noo mo-« p**0» ^»*>#fn oo>« m#—ao c^^-*^ ^-^*-^ <t--o -r.^r» o*<oO »o*n#-^ 0>of«4« *« 1 'j^ r*«| wiLf < UtA4l «M^"» r*«>fM »»p^-*i r*o«C 'T*wn| -*— n# m -r aj «»#»r%r» o^^i »-•—^ a?—-^* OO*^ ^* ***f\ aoaoaa r-*—•-- r-rri OOO <r»r>*^ 1 «*4.
4
C*o»<?» o«V OO«0 f^*-^^ »•*«*«• ^**^» <o aso«J
J 000 o 00 000 ^ » * ! 1 1 1 ivrvm »n**v«># «v»>m mm«> ^#>-#'4> nmm p»^-f» ««»<o opo «vn*4
f^ <o w^n -**r«c* oow 0-^»< Oo** o«>-* ^h^p» v\.r<*>4 mr»jo* ^«?oj OOH f*w\^ «v*<n o—«*HV* «\ mo Oi^"1 «-*mo otoo -*—*•+ -+•**) aj^jr^ r^ncr- m^ v f*cr>«o -o-^<» <»**^ r*«*>r«« frt9«4
'O OO^ *N t>#^ irw>.o *»o>»^ • *n| mnm o*o»(^ wvr* v»t^t^ o-cc 4> -4> '*' •4' -o -o -o * *0 ooaooo
O OOO OOO OOO OOO »»«« "N. IM M+*+m4 *w<*>4 r-4*>gr*4 «vnm ^ «r»w\»l -O-O-O ^"«n»« 0*<?*»«
-fl *» ^^ -»-0^- »*«M*5 r<>09 W<yO J5«^-0 fno»o ^o-*" o**« ^0 o-*-< O^-fl ^^^v0^ <?»o»>j-r »• «^o *Ood f*«noo r«ioo oh»n no** <J^-*^) «-*o-0 >o-— r«- r-*»^ o ,»*'*> ir\o^< od-*0 <*\*»r>(
• t t • • • « ••• •»• • • • • t *•• ••* • * • ••• ••• •*• • • • ••• • •
O OOO O OO OOO OOO OOO « 11 I. 1 < fMofrsJ r+r+r* fTvn»n *•*#"# ««m <0«-0 !*-*»»»
N 41 ^e>'«o t*-+m w«o «*%om m»^^* -ot?»*n f»moo *<>«% -om« 0<o<# r>*o^ <o-*«>i o<vo»O r^ r»— in ftfvo f'V- O-rO o«ao«9 (»OV\ v*<x>-Q 0<O^ o <i ^ O^* -r NflO «*—^O -OX
O^^-^ O ON •*—«f*t P»n« •>*>•<? f*r»OB OVO *vr^rn ^»"r»0 C^<WO <T*^ OOO •OO'^ f«« *-«?•<• ••• • • • ( 4 I «•* It* • • « •#• ••• * • * «•• •«« • • • ••• ••• •«•O OOO O OO OOO OOO OOO OOO p<6» I »* «p^ p<i 1^ p*-«f>| »>*)r«#*N| f»Ks#m fnfn«*> •C'* »»«o«n
« 1— 0* A**>*-* •^oo -o»sr>J >m» -*-t>^* ^-^rt Q«to o<N»*n p**»*Q •*«»•<) »^'y**> moo^~ *> r5"*f «mm —^- -*j r+*Mj •+*r\U* v^pk o-o-'-' aumt* ivv"f *«ri^ h*<*«J* 0"i^ »-»«»«.^
000 o o-^ oon -^»*m »->r^^ -* ^- -o oo'* 9Q9> -*o-« f>*n^ oo** ooh mmm r^-«-* ^*qd4d
ooq ^ 00 t>ao 0^0 000 c^oo 0*00 000 w *>^ i^ *^* * ******* ***fH**i f^»*»*n fn*n»»i
• o h* p4 mnm o<4>f* omo m-#N 0»mM ^e^ o*^»^ o*'* «tvn#»j> «fN*o a»v\*n 0—0•rt O NO h-^co »epi* r>Nao oh.H 0-4>0 mfV"! l/»*»tft «i^o i^m»^ •rr*»«* t^^*r»t rv*»aoN OOO O ^I DON OO'I N-«^ "•'n-C *^0 OO 1"" <D<a<7> OO"^ fnf*>* oo*» 000 *-*^*» 000
K O OOO p OO OOO OOO OOO OOO OOO OOO OOO I > I »« f+ *+*+-* r*rsir*i fMr>*N «^»»>n
k» o o »w**n irv*^- —"0«r* ov\»4 noo ^»oo-«* or^*v^ -*mo *> «ooo ^9^ o-*oIC -t cr« >r. <~j h(d9> mo** r>rs|p* BO ot> ^-^rs* — <x> <?• «4> rgo O^m 0Dir>»^ i*^>0 *r*aoO N OOO O OO OO^ OON "*ON f>*Nm nm^ ^^iA ©On a>f^»a) OOO m*vrn tninO 000* m**>r>
• • • • ••• ft)* ••• ••• •*• •*• • • 4 ««* • • * ••• • • • *•• • • • ••*O OOO O OO OOO OOO OOO OOO OOO OOO OOO OOO ' * < *-»-»-* Hp*-i « rsttvrM
v* f^ — * m> tj ^ h«# n«^ m^*^ rv«j»r^ vimio mm« o-*" 1** O-rt^ <*>«c 1^ « r* O ni m 1* v»«nN ^«if- «»-.v »c*«x *n.-* r-mw iw-u ^wn i>»vr«V -^ OOO O OO OOO OO^ OO-* OO-* OON P*-^m fNirvrn r>trr\*> + r «-> irt*r> O #-».<>*-• tWT* —»0-
<^ O OOO O OO 000 000 000 000 OOO ooo 000 000 000 000 000 000 **-»*
• >oo 0000000000000• UJN^r oWON-C^ooON* o«0
43
0)
wId
u
c
>1-1
0)
ua<D
T3•HM-l
aou
>erID
Ui
oI
o ••••«•• • ..«•..,-• «4 »* ** tM n|
_j m h ^ «r m <o -o o r~ <n (7> -* m o» <oO m in w» <•> "» .* -« rv) in T 'JA u\ -^ ui (_>
a-oj-~oo<3 4, -o rn rr'if,'iA—•'-•la*
r»iv;\/'v<vuPii-*<Ohnuu>-^u*<or^_i-^eorno>r>'T>'HfvrjcorO>n5jr»io<_>•••# »••••#••••
—• —« —t —• cnj
O—'•-«rNjrnfn-*u-\-or~^Orgini-.o-* •-! -* —« fNJ
O^rNmO-*O-0u-te0u"*a>»-«e0C7>-or~Oco<NjrgoO>'NJ<D-*'m>»'-«>03r»r^<orNco~r.-<coco<7>mr»r»-*rM^••••••••••••••lp4 «4 >H
a>aor~j-o-C>r- r-.u-imr~(/<rgr\<0J4)h«hnivoi4<i s;ior^r-(rn\nO • • t *••••«o—'—•iNiojrnr^^-j-i -o r» o» ^ m mH •< »4
<MrNPiN-r>gr»^v<uj*>«-<uUH»iNvjr»|cr^-'-gr-rsjo..-r| <^>r->oa3 rJ-j--r •ow»o t_> ~« »-i 'n <nj pi pi -T ui <o «* w <— r-\ m
'tf> «-« O *-• >T fNf""Nj- v »* rs< cn m >« mPI W N -O O >•> O •<> «*l P4 "• "I r» * *3* •oo©«*•-<^M^gmm•»• in 4) r< d o in
r» m >o M W O ^.^0 «*»>»• •© vn n» <\j r>J m0<*'-HO>», co<\IOO.e^-*mmrx«0_».... t4JOO»*-*-*<MPJmNv *• U> •© cO 0> i-J
ir\H*«-«OP*'"*>*>«u>«itiir»inrN'f>iP'tP) uu ui -y v/- J- i_> u\ ui —< v UI <^ P| UJ
if* PI r» »-• u> v* *ro«~\rv»HU*-«u*>^oC7OO^<^^rsir0r0uftn<Qf«.«o<^
>oooooooooooooooujr\j>r«oioor\j>r -ocooin-t-owo
X
H4
V. SIMULATION ALGORITHM
A. VARIABLE DEFINITION
Tx; ={inf t>0 ; Z(t)>Xi }
where Z (t) =superposition of constant load and shock load
Nrow=maximum number of level X; ; X(
<X i<X i< <x*aw
Ncol=maximum number of repetition of generating T*
Lc=constant load magnitude
Ls=shcck load magnitude
Tc=constant load interval
Ts=shcck load interval
Ipc=ccunting the number of repetition
L=counting the maximum level of X;
E. ALGORITHM
Input parameters ( XrMt a* b, seed numbers )
Initialize the stress level X;; X,<X i <X 3< < x*u,*
ipc=0
Repeat
set T o =0
M=0
TTs =
Repeat
generate constant load;Lc
generate constant interval;Tc
7ind L such that L= {sup i;Lc>x; }
Set Tx; = to for 1<i<L
M=L
Ci=Tc
A, generate the shock load;Ls
generate the shock interval;Ts
B, If Ts>Ci, then
45
TO=TO+Tc
Ts=Ts-Ci
TTs=0
generate constant load;Lc
generate constant interval;Tc
Find I such that L= {sup i; Lc>Xi}
If L>M, then
Set T*;=T for M<i<L
H=L
Else continue
Ci=Tc
Go to E
Else, Find I such that L= {sup i;Ls + Lc>Xi }
TTs=lls+Ts
Set Tx; =Te+TTs for M<i<L
Ci=Ci-Ts
Go to A
Until (L=Nrow)
Ipc=Ipc+1
Until (lpc=Ncol)
End Algorithm
46
APPENDIX A
COMPUTER PROGRAM
*****»*** -^
* rg* <* 0: -»
* X « NJ"
* 1— —1 <# < a:* X O t—
1
w« Z f— _J* -J h-4 X z <* LU 1— h- LU >—
»
# > < z >-* LU CC z a z* _l LU a LU* z 1—
<
X z* oO LU H- LU# 00 O 3 a* LU CQ • *
2* CX LL -H ac* H- O a: LU
* 00 X 1— 1- .»
* 00 00 LU a:* OO -JZ •—
)
z 2; LU
* a LUQ Q a < i—« LU >-« O —
> cC LU
* LU LUh- -1 II H- < S* -J< >-iXO—"LUQ. <# X O •"SI- II hh a:# LU CO—
•
I- XLU<LULU<* »• 00 _) LL ^Q_ OCT 01—0.* * O LUQ.LU LLO LU Z><« # < a:u_o_j O LUcX-Jt— CtLU•* * O i-orrx >o <—
«
Q•* _l oO 1— >'U l-H- LL>Z_IO# ll—iqc:q_) X z~< >0'-"0<l-# 2: z olozluzx \- <_i»— aco*-*# a O Oh-h->x i—
•
—•0:0:2: —<z* <—
^
*-H o:<z—iq:v-ll 00CQ_ILU< QiO* h- t— QCLUJI^ZLU z< —<CQ QQJ<# *^ < LUCQ OHU. '<iocqcq3:q<<s:«• z Z icyQQ<zozau30<a•« —
<
t—
«
2:z><<2:~ << a:cazo-iOQ« u. cojDzao ZLU^LLQlO _J <<* LU SLU2! JJQQ<S a:o t-oo* Q o> 2: << LU 1.l lu a. ?• h- 2? _i -J» t_i LU 2T "5 1— V- C3O "J" LUO LU _J -<^<r* LU J -3 3: 2: 2: -1—1 _i :o a- lu>-<>-*;*:# —J LL 2!i-i<< LUO-LU-IZ ZJZH-OOOO* CD Ooo~ XI—H-^^DSD<< a:3i^ZOQ•» <I i>o x< 00 00 ( _> q:< —1> 00 t— aax x* •—1 LU lu «q. 2: <C^ (_>>-/ >—C)<t 0000000# QC 2:1x2. UOII !> 11 11 II
•* <5 —•1— II II OOOOOO 11 11 II II II II II
»• > H^2_| • 11 oca a:* II OO II II II II XX Za:a.O.-t<NmrO# X II a:0-J'-<—I—" (— 1— i^LUa 1— CL<<< <* * (-XZZOU^^Haiu)Q<h«ci:a:a:cil# #* ** ** #
* o* o
* zLUQ3
* LL.
« o* —
^
* o*:* ^HOO* — »* X-«* *o* -JO« X-t* •—
•* 0:0:* -a.
» u. •* »—
* LLO _»•M- »rH O* _^. o•» oox z•» * —ILU 3C
* * 00 » o*«.—. o:* * -to z* * 00•* * »r-H LU* -1— _i•» ox •-•
# 2: •+- LL•« < —I .—1» o: o »o »« o 0^00* O 0<"^CL« cC inn?——
1
a- .» .rO -t rnmo—
'
# z <M< »^-i
•M- —< —a:-* * -^rsjrn-t# <i x «02: <<i<<mr-p-p«
« <^o:oooo^>^ >«>^»mr,-n)i>-m•»• sfo:—-lu t • • »oooor«-Lr\t^-rn »0 O*«•«• »o:o—*rsif-tr-i t • t •fNj(M(Nj(\io • •
# « _J^-tQ.LU 11 11 11 (t -^.—t .—1.—• H II II H IIO^O
# * <<(— f—^fMrnxT II II II II .-KNcn^r—l II II II
•fr « LUa:i—^<<<<—iNKl-tXXXXLUJOQ# * o: •"-! 0:0: Ota: LLLLLLLL -imciwQX -J H-
*
OOOOOOOOOOOOOOOOOOOOOOOOOOOO
U7
LU *H- *
• < * #II Q£ < *_J a: *
> 3*o •» *
•—I > •» < »aC 1—4 -I CC -^ «.
% a:-* a k >t *QC* o <M < *<— 2 < CC #
1
Q-3C
or•
1— tJLU O r-H < *Z o~ CC < OC *< r- z DC »•» •i •»
\— 00 - > •> H U *oo • OsJ 1—
•
a X o *z * • l_> 00 X •b #a xo •» > m o *o —IrH _J X z #* •-LL o GO H LU •ft
•» "-«» » •> X oo Q *X •»• vt > -—^ •* •» *t-\ - II X •» XcO ^ * •^•» —o M CO h-Qg -»»o0 * CM^ CL< • CC XQ. X » # UL•» XX ro a. < t-x # i9 LU X m X - 1— h- * 1—)
* *-_J *-4 Q h-X »»»— * LL
# > 1 «k o oO 1— h- *t •> * *>
•^ <M o » H— <x « —1 «•»
(MO X o> CO X •—
•
CCh- * U "2
< •o >—
i
X 1— x-t »LU * -•—
.
O«frf- ox •» a •» UJh- <(NJ * # _I^H QC<< f-iOO —A I— -1 ujq:<_i * O— -* -^ z0£O LU- X O _l * aca * CO O m
•h •» —
«
a o 0_jr\j -o * CM » •» k —1 r-t
rot- • X • o z -»UO<QZ « X— H i-H H O<0 II r-A o —
»
m -IZOQCZ » # l-tr-4 •» •• •» r-t
oca o » Q. -» Z£ o -z •LU2 •»• •« »^» r-« ^-( —I-z <-N. •—i i-« o 03C ^00 * * r-*< •> te a
c\i>-t SL - k + a:->ZOIO -DC * # X < CD H< >• o _J Zo! tfOoi^Z «• * •—•cm > •» X ITcc*--_J—
i
-J o aizoczo » * w u. —
t
CM — -jo aH»2IZ •> o XhO -2 • OCX * H • X X <OQC
rH OhOS X zo h-l-OCX -*:ZI- * oo 00-^ CM HH •—
•
Q -Z -»
<- i^zi/ia 1— wO •b »ZH Xoo » «k » 2: ZLLX ««• —
.
2T-. -» ^or* •>oo<Tooq' _J •» »CM xro » 1.1— •
o^^ $< n *—
1
Z-H^CM MO^ it?
LU X^J-O -axx »x ex 0-1 • CLa.auu LLO » —nsoooo •»Q —LLLUO H-O-t-— X*- «r> * O OHX# X* -H—t Xi—i »azo.^ + a " •(- o<-3-<xa * O LU ••XLU-".'jj-» LU^-»>-» •
OpHX--a— it _) rflO Q- •'H-O.Q.CL —3: * a Z—1—
<
OO'-^OO'-^Z 2X tuC3 •»<—• O" *"
<
x; >—«UJ ^u.Q.aiiiixa£i<i-u * a. HO . ^-Ql 1 aooo^« •••» •» II —O < hODUI-OUU^ZU * CO i— ot:_i<_jcD3 1— 4*LU3 •
i—ILT\wh-CM MO -».xz C£CM—
.
ZOhWOOol hhQ * Z3 Z3<MJJ_J II -III h-Q o# OOJ•-H || || UJ< •x »o »—
«
II —
1
U.LL >—• • «• 00 O* 0<—*<-iLU^ O—ILUQ^OII -C—II— 3IO--<0^—
>
_Jh- -J *—
(
(-JXJJJJJJQ. * a:_iiuuouootuj CC<h-Z—OOOl-.c£i-| -r-K XX2 J^H Z_I|-_IJJJJJQQ * CD<.h- djuj^ 11 u.
a.ccotx'roLL.'^LLO D <LL 0<LU<<<<<<!-
2
« » Z5LU2! O0i»-«5tfHHhZZ 5LL ». » —Q O o •» KJ^J OOOOOOOO LU •« * 00 Qtt Hi 00««•« •« * «• •J+
O o o # •»• «-«
r*- o o o # rH—
1
l-l CM c* tt
o oouoo O
4 8
00a
1 H- Q1
m 001 _j to
1o •4-
1 o LL1 z to
1
1
1
1
1
1
1
1
1
1
1
to
oaczrH
o-Joto
LLto
<NLL.
rH
LLto
ai—
"*1 X Ova- 3
-J 1I—
1
ox oo 1 K i—1>-( oo
1ro —^ » zz 1 X xrn •k
»1 H »X i
2 1•» •^H oo 1 <N l-t •> a:
£X 1 X —r\| zz 1 l-H QX— m
to I» *»-tC\j o
a 1•—
1
— »LL 1—H- 1 X r-H—H •• o » 0>»
1 H _X-< o -•X oX i-t 1
•i 0"-«LL c* 3TH-00t— O l-l 1 o •»••» o «o•«_J c* rH 1 Q. -»_!>-» a QiOOOuo rH 1
rH oou hOZH -»-•-» -»
0.0 o 1» oo - r-t »hQ OO O
—Z h- O 1 O OZJ o i—i »S—O Qs b ••
to to h- 1 -J in »o OOmh O •-• >H—
»
-"i O 1 to *:s * -^ h- H-tO-»Q » *o —o o O X LAOCVJ -* _J "O— (— -4 pH*H •a; ^, o h- r\J acTX ^H QOO---I * »uz "^—
»
-* X •k «->Z_ + 02 + 00 Oa -J » O'-t as k- X X » * -J—x«-a—IO - •h- «—l |o + h-O W (— O^-t o ——<ro;o— ro sj-
<rH O-J II a: LU o »_|X UO<LUZOJX Xa LU •»mo "^s I Q _J »l—
1
Z_IOQi iZQh -(
o a:o •o zu 1- Z oo<- —
»
—2O C?— QC—rO —>r—
,
Oq.lT\2 «CLC? < •CLr- •XmK LU •zzu.zu.o 1— l-H M«— o >-«LU LU C£-".t-»H-«00 o> • LLOO «C» »CL* Q--»-*~m to •• <—> • -j » • ^ 1— -tO z -tLUh- —< LU 1— X ~»X -»
a»-< ZXUJ ii•—••—< o^ < LULL QCO o • _I_J_J'-H lOUJHLUrH
LU Ltl h-a i-h w—» LU-HO + z CC z -4-UJO o II o •JJ-O «00>-00»-<-t »C_J zra: • XU-^ + o CC LU •-rn-H- O • t—q._j<<li_q.o o a
1^1- 1—1 LU -ru or— *£>-* u"-o _> *£. (— LI ILU_IOOrHOO>HOLJi_>'-"-'—I—I II —1 II
*:— Z h-o^cl .—4 HI—
1
t—l—< • 1—
Q
LU ^ »<!-—1 11 ii II >-»w— «-.w_JI-._J_J
II LLO OC IDLU_J>-H>-«rH H II II o *-tlUZ !J 0(MLUZ<'-1 QOQlLU. LLLL<0O<o0^"-•CJ3^3 D|-<-M ZOOO II H q£uj c£u_ q:>-.o^ 00 _J (_>>—< i-t >-i-^o o
II t—
Q
aZLUU. II o a_ioaou CO to
~<iuz. CD-* ac*-iZC3 o <—»l
—
_l a*-*-»q:uj Z5 LOLL
00 to
#rH o »—
1
i—
«
Oo 1—
»
f—
t
O rH1—
1
1—
t
1—
1
ooou ooo
49
r\l
O
o
Oo
o:(Nl
O
3o
ict:
~i O•—i oO* +-J o0~«l—O— II
oo
00*—
t
Qo.
•
o
O-iQ£00Z I
•I—I— 00
_)— -JO._l -=X H •—
«
—Q^ »UJ
0>—•(— U.I—<X>—n—iOO+ 00—1 fHt— t— "-H—J II O_i+ t_i z: ii — h-h-oOOO—IO QOU.WII 000<0 O —MHO-J II OO OOOO'-' OO^U.
X
ooh-•—too
• o<—
•
OH- OOII II IIQQhoo H- O0
OO.O II
H-OoO_J~t<oOO
oo
3oa:
c*-»x0:21—o(NO »o
qzq.H" »!-•
i-h »H-O 1—•*-•
o »->o— _J »o—OO—O »_I-S-IXwQX<LUZ0>•Qa: »0
"t-ZOO(NJJ>-it— UJ• U.00 »0
-J •-"•—UJJH <—00—0u_<a.<u_o o«-«
II II
OO
• +o o o
OO II O •0©0-• »h" »0 • • ''oowo II OO II
II *t•—
• II —I II II oO t-io hho _J —1 a.
0O0OOOOO 00 •-»
<7*
o OO O —
I
oc ~* o oa>
o
1
>*—000
1
1
1
1
1
1
l
1
«or\J-H
00—Q «X00 ShZ:> Olux•> 00 • •»
c0 »v^-»x o<o
l :> ooq:o •»
l > .—
1
Il cq »r<"»w a>1 ct co<ac a.—l a xcca. a:1
m. > »h- LU<1 O »c\J|— oco1 00— CQ<t » CC 1
|Xo£o£— H-X
i coi— a. -0 »j«
1 XoO *-^0 OC1
« ».Q<t-t -»<l
_jac"ooa£— o>OQ. »-CQ 11
00 OH- co cO a: XZHXSQ.Z H—
1
1—
1
•» » *.| ,. <^ ft. —>h- 3c0— - »_J CLLU00 Oa:o<o » O1—
•
ocaosu^ 1
H» Z<OI— •» » >H-< *. •.m »o-j UJ00H XX .su » -i00 h-h-iT»h- —
«
1
•+-CM •—• > XLU X ••—1—O—
1
- cC-I —XX »oo -<.Q. t— 1— 1— (NJOO XC0 3S
S Olu -Siaz rH | O< Q. p»-^00 » •* X CC00 2I-4-0 -ir>3C-->» Z
0<O^MQON.I-«» •>
UJ O0C—<"3—C£0 » >*<-•
X — »xz:>ox 11
h- UJrrix^-h, •h—1 > 1—
1
Z< SoOQCvO—LU •-•CC-^OO »LU>-H O(— l__ «* »—»0Uj<Ici£^»O
z O OfN—l>TOUJ|— i<l 1 rH
QC Q. O< <x 00 H- >-•a. cu u.
O 2: oictruji—Hzo:a 1 luoH-Q co -a: •—h»2u.xqqwz J—» HX - OC£LU 00< 00H- *•
QC 1— h- X-«. •> >f ** * «
a>sO
o> 000
50
-»1 * -^
1 j -^ -•<z 1 •—
•
^-QC* 1 *" X 1
r\l 1 X » —«^ .» ^ si- a.* <xZ 1 # CL •»• CC\U# 1 X — •»
m 1 « LU » Q.rn -»-^
1 # x< -•1- 1
-"» ro -*ujq: z<
u.«•
<\|-»* CM
l/)U0
1 -1 <1 II c£.
1 CD +1 II —1<-»-»
1 -J—X1<•"-•
1
rg | + X11 o-< 1
CO »< —
»
<—— -«
ro-» x-Km •«
^ 1 hxa I-O+ CL*->s 1-4 -J 1 z 1 x Z •'H #1 -» O a 1 LU—LU -» LUC\J< O-»—
1
>* 1 za# 1— co Z + QC •« 1 z 1 ox— *2: O—— tNJ
—
z
O w1 Q.U4-.-.^ a. -»— •—
f^w 1- K 1 x*^,^^ x-»o 0.*h —
«
< I Lumx<< LU>-iO Xz< O -J a—
-
l <* 0:2: «-_j LUin #0 O o _jCQCQ 1 jtumsH 1—x< *• <\l_l —
»
LLora: 1 < +<rci^- z# 1 <-•
(M >* 1 u. O z SQ.Q. 1 0—ia£<-H- LU^--» <* * # r\j# • «-• —>> I
—<< | QC-* cc<* a:* * * *<t O H» -^—*<^
1 l-Ci:-.—— LUCt'— w—
•
-^ —»-^ ^ —» * — • < CQH-I--* 1 Z—— 1 (M LL# X "^-a _l ^CQ CD *m Z>x O O c^ctror-* UJS-»-»* u-o-it
1—• ••>r •*» o •X X H >^-^ LUO _J a.ara»»-i Q—»-«h-H».
_»<-• -1^ 1 1 1—— »•-» —i - •© u. l
0000— Z>-iro—*>—' iH Q(M< «~l
o— z O—
»
zzzz>r 0_l-»-$" V. 0* # X < <XX< ^.QC «.
ox — UX^ ^ WM—#Z _l "^ •mm* i-uLuct: 1 -fro: uua.— •»
ZH- ^ ZH *C\ "vf 1— 1— 1—
»
«- ^ z. —t »Q 1—
1
f-4st-r<M 2:0;+—.— OCX* z»+ < • 11 -•</: •—II/) <K<<Q-» m —•-•»— r-» 1-4CQ— OvO<a: <—tCLr-lX. <LU-» X^s: ^-^.^.1— — 1— OOOOoirg r*Xw + —a:* • • rjjQ-UJ <X<— + -H *.
113 -J CO II *TX + X + _i_l -1 _!— •«II HXO t-t t— Q-CQi-HrH 1 H- ^~»GCUJci:— —o< —
-^oolullx ^ »t— <NI|— ^LU LLU.ILU. | # J II H-O>-tLu< 11 q: 1 4"-» II CtX— 1 N.HH x »a: ^O ll^^sll HH«—' 1/5 —003 ^# -J-O x^» II DO-—Q.CQC0Q.--«t———t-KT)^- -HS <.o2zr-»ooo«- II II II II Z—lf\l(NJsl- J-^500 Ot— Lt_ >-»Z-J»-«'—C*:c£X*-< OC_5«—<X O 1 — QiOO")-h^5« • »OX(M(M^-t -»ni/)LOi/)T-'— 000—
t
-.-^LL-— II Q.G.LU-— LJJ O* Of— — f\l "S.
il c\joo»— uo~-OO^t-l'lWWWhU- II II 00 II II OvJ- h- 11 coco 11 11 11 ixiQjH>»a a* »•
2: Z II X II II 001— 1- ZZ II (N>t^QcQ II ZcooicCrH^aro-i—z<< + x z^# •30 OCOh- (NJ-J-O O II 02:2:—i/)X~iQ oa:aQ.jDQ.h < 11 q:^huj <<m >-i
WQ OXLUOOOOQ o^oooooo 11 >>>-«o uaoooh 1— i-u i— 11 11 >- a:<5-«—>r —-• <.CQ II -» II ct-» 11
3 ^?x 2:2:2:a— hi— 1—
O0*
xz-»s«—X— h-
# •«-f\jX
»• +*
O -«oO 00<NI rO 4-sf OOOOOOOO
51
oo
a IA —•» o*
-^ •
o a* ao c*-• 2*—« •» *^ CO >*\OO o * »o>
2 * Gr •-*. «k * arO Lf\ *
> -»o oQ X-M £.
O (-— X•i xx on i—m
CO •>i— on f- • aoX xi— or z CJ • <^> h- •o » U. O ^> i_-» •. ^ O -JQ •om— <\i w
00 XO^OZ o.•l h-^On •• ujon i <^ -• <«. <•
r LU«-h- »— -JfNJ o in ia m ot- x »oor\ •-• »on • cm r» o> o^•k _|l— inin—4 i-or- r-l t • t •
CO Oujr-^^- 2 • *- O O O OX O OX'^ < or O 1 1 1 1
m 2— -H-Z o O O O o oa:— »o^x * a —»_J • • • •
-^—
*
a.>» JCOfNI •-! •^< i-4 i-H ^-4 -»
mm i— •» QOOh (\J —» _)-«• •* «^ <^ «^• t ••in cCint— u_~5 • _J —-» -»-»-,-»-^ o o o o
O"^ f-ti—t^Hr-4i-< O O O Ooo CQ • ijj 2 * •* • • #ON —
a
** cxo _j »LTMnO> '—
1
* • .-»o 2— U.LLU.U.U, —; —1 —J —
t
## Q.-4 •—
<
X(\|(NIO » 3-* —2 •*x ##«*# < < < <CO CO -U. i— 1 OCJ-J n» h-—
»
-)h- -»mLnm co o-*•*-»#-»«'—« -•XX -»r*- 2 »X »HO •• <I-Z C7* <—h- _KMr«^cM7«cMn-»Ln-»iA-»co-»oT>>:> »—• < xh-~» *o m • a<aa 1 XI O • • • • •f\J
-jr*-->0^-5C7^~7O>_»w —(\j O — •.LOO^Z —4 0^ -IO- 3—11- II OOOOOOZ-2—2w^w2»•« x • Or 3-»--40> * X • 0> LL-IX O II II
-» z-"-—'*-— *x -X »X -X »LHlTi — •4- a.o*-0'3 t-tO'vO • *a.-' a£_j -*_iLU—X XX X X ->f- -5 1— ->l- ->»— "3
^^ Q\Um LU 2IOO* »Q-* « «c?o^^h-«- u_ 2 _J«M 13 t— 1—1 1—• •—1 l-H 1—1M |— —• |— ~-1— «-»h-—CDSsO^OcOO » X 0--4t— coa:r\j'»x Of • —%—
«
»>t—rjr2<U-U_U.li-LLX 1 X 1 X 1 X 1 XXh • • xsy I— o*— ».02^ » —40*-« n ^n(3t-l-lO>-W«MMh. || - || |— || J_ || |—II II <-4r-4 -X »'-H X~»^J x> || || w-» II -4 i— -j ii ii ii ii ii ii on ii m ii in ii oo ii—— 1 Q'O- LU LU ini— 0£>O'-4LU •—t—»c^>-^UJ-) 2u.iAinincoCMnr\iLnr,-Lnc>coo>o>i—
(
<—i CO LO 00 —* h" t— Z<T<-t ••LU-—-_i ao -•II-'3 o O 11 r\ir*-aN 0>C7, r\lor*-O0N Q'0,*CJC>—XX II UU<LU O «-h^ wco'jjuj^i o>—t^»2cyzma o-'Zzzzzai-en-ai-oHOXX II II >h- *--3 o. h- -jcjonujt—«ixm •oaw^—
<
o u.h^_l30«QCZZ 3C 3< ••an— >-<z:- »c_»f-« H ^^
hhoooo:omc< O OLU-* zaro: o- 23:u_h-0 o ooa:Lnin>-«;sox- § OOZf-Q CO i-IO^ LL"-1 •< UQ .
OUJZ 3 «-CJ Xoacui 1
1
1
1
00 CLl— >s.lA»s • •
c*o1
1 «N —i vt
oo •H O or-^ ^ i-Hooo
52
mor I
s- m
3 -»
-o a3-« in
— 33 h-
3 3•> I—
m —
oI
oI
O f\J I— I—• «— • «.
-H 3 -*C0
O -» ro—
3
O r-4 »Oh_J -» — cot—< -> -«. 03CML **T\-*«• -»w-» a>mao^ -a^—o^m—•
-5XCT>maOO— O0>3-»3>-*'^3 •
-5-1 •VCM^OOOh'J * »—"t— co
— XLU333 31— I—I— II — C0<\I3 »u.X II II II II II II II II II — XO> »H— ">tI— -*-»-»-»—-»-.-»—.0-»3m-»0>.-it— ^-trgro^LnNOfN~ooa^'-ico ••u.^«-» •
I-»»••»•.» »<om -03X
II -i -j ->-»-»-}-> -j -j-j -OX •»>— sO0„—%<—— oO^vO ••«* (— o^-"— "Qi »<-<> O •"-iCJ -»<1hh^>Lu ||—»Z>QOXXXXXXXXXX— ——^h- X00>2>0-LU O^ULO^—I II —Z II r\j-»_»z-i
3^1— I— I— I— r— I— r— I— h-LU—•(— LUC0< LU LUh-h- CT* — I— -J COZ II '-iZO^'ZOw-OJ-mU.t— xxxxxxxxxxh-c^<iH--»2:uj t— z < occ lu<i i o— -> ii it —ia.arzi— ~j—»—3k- m
QC3QCixi—ozz cl >— #-» ••o^cc." iu<ifiaao uxa«uu.^ »o:£ fcU-t-ioc s: :D_jmooi-ua:o -& oozzq oxq o— LL. in h-3 O 0<'-<CM— JZU.X* _J<-lao r» zt—Q o oclu-oz ih • u.— 3 ou-12: cQa£3f— •-« »-x ii a3 (— OC^LU 13 << >vin» LL.O
# # •«• # # # *
m i <n ^ (\i
03 OO r-l O O
— ("0
3 —•• 3
in >—
CM •i
3 ma*•» (NIO— arai
1
I
1
I
i
1
1
1
i
I
I
I
1
I
a. oz
-» <a »oao ao—t-tO O
1 -3 ZXrO< <Xr* ••
a. m mx<<7» a*I— »3 Z00— h- <coo •• m
• ••«• m
•
3X
•
a «o3 •
LU 3-1
h-
ZX oi^-im f*- <(T>H- Q.wO>-«Z
<lX'JO<D «co33 •
LL •t- <X^M * 3O xi— » »m
k »inorsi-I< ,_^
LU H-»Mnz Z —
»
-J •>03—< Om -J•-t XOHH » >-i(\i w1— 1—^<X-» i— »m a.Z uu— »xm mON << »xin »<-« a • -^
i
Z> —it— r»-—
w
2 3 -* o3 0LU30 3 a -> •
o »<oz o <a« r-t
_
I
Z-» "^< •^•^ CO •»•
< •oin^» •• r\j <NJZ 0£ oZ 3IOMXJ * • •^Q.3 Q. oa QhOX * #3f- •^ «z< < -»_J>—» a;— h- »™J • LL •«-»•—.
1 —
<
i- 2)«H * 3— * f-r-X O -l#i—
«
•• . fcLUi—
1
n» ••• <<-. • —»—
»
Q x-»in •• •» •> * -J OOU. i—
t
3-»Z h-OfMLLJ X - — -I-J'-' *- z-> -*
a -03 -O ^Hr-« f> CO OLLLL. + *v <I— roo xo^u •> t 0^ QC-t^** ^ -»p* »x a
—in »a>z V.3>0 • saa »^-«—»a. -5 *->x za. —»3 —-^ »3 o<z i—i ••—>z —^— |
—
•
LU xmini— 3f\j 3 -^.a:— 1 11 O— II X II X— H-X OM-KOHX J7XJ —i II CL— LUI— _lh- II LU<
00 O' OOU
53
m m m CO 0>og r*- o> & 0^• • t » •
o o o o oio i
o 1o o 1o• t • • •
.—
I
•—
(
1—
1
1—
(
^-*
o o o o CDo o o o a
-^o* —
«
vi-O v*"—3 —
•
3< a< H-»C0 < o>
-»;j\ •• a*roc? —» 3—
<
m Har «_» <«im 3 »
»0> 1- 00
imr < of\l< •• 33 m »—<-» <N •«»0> 3 •—»<M K- mt\J3 < o>—< ft 33 - —ft 1—<-- r\j <•CO n* •»
—,_»-»3 *»
-*3rOh— o>—< •< V*3 »C0 3<mu.-» 1—••r-^rH <——*3>—•*•
'
•TO-» o~»< "3 —» •
o>mooa>>- »c\j(— coco
U.LLU.U.U.
mmmcoo*rsjh-O^OCT _^j t i i _j• • • • • <t «3 <t <j ^COooo -»&—«.-»•«.-*#. -»* -»
«—w———m-»m-»m-»co-*0"*— ">*
MMMMMZ-)2-5Z-)ZTZ-5-)Xs.CM^(?aOOK^Nin^ 3>tLLLLU.U.UL <»-<-»<—<*—<>»-hOOOO|- 1— I— <0*-»U.V> t——*
.-_.-«_,_ »x »x »x »x •>xxuj<«<<<< ii a^3 *o» < •»
+ + + + +• -sx-jx-^x-jx-jx ii ii ii ii ii ii ii ii n-»o^<xc*~• *xiH-^HHH« I — I — I
~- I ~- I —,—.—»—»—,—»——.—.O •» •—H »s0in>Oo. a. o_ q. q. x «-•x— x—x— x— i-H <m n ) <rmo r*» ao cr .-• vo -- «-"0 «— r>- >—ZZZZZh II h- II h- II I- II H II »•-»---•• »^ok«-OOH-ii ii ii ii ii ii in ii m ii m ii co ii a^-5~>-5->~5~>-)~^-3-5uj—<lui— h-<mmmrocMr\r\|ir\r— mc^aoaMj^cr*—-*——«—>——•——»^-h-c?2:h- <x <xujc\ir-u>tr>cr>(\ii-*i'-(j(^ua>3U^i-#i— h-i— f— I— *— H-»— h-t— «-i«iac.»-t * *<z.:dzzzz^zot-uhOKUh-oh-xxxxxxxxxxo: uq:-»'*cjzq:««<«««««XXXXXXXXXXi-»U..IinNlIHD
m —— t—t—
o
— 33 ZLUZ3 h-H- OQCUJ< << o
1
1
1
1
1
1
1
1 ct» •1
-, ^ -j
1 ino z •—1
1 h»Q <1 O arr-< 00 i—1 Z I——O1 LU — «-J(^ z
a om<^3 » zm or>« »i— m >-^
z x. >-4Ur*<l U" QCo <S) «— »LL » Z <—
<
m xm »co » ah- X hr\l£M3> m T.3 h- 1— CJCM3<\ir«- OCO f- »^3l-<Z OI—
«
k -•ooh— <a£ * N_
DC X O »oo •> »-in
— 1— om »co-*f\i LU00 LU hmo>o>oz —11—
<
* -00*00 * •—
<
Q -J Xh-31— —•-• H-O I— »h-<—m Z
-J U turn » ••i_)<-t <h z. •M0MftO>« r>< •> —30^ *3 3H ^ »oaiiAZ
0-* •+-o,
> »u. or Oinco<3_jo z mi—io> *>>«. *
•» •»—3min-j #LU X in3H-r"-r^ » *-J h- (\ii—uooa«1—
«
» —•00 »t—i— •1- X X 00<o0_| *z ** _-.tr •• »o m< 3 •>m3in— Xz> Q. -»-<|— IAJOZ r-H
3 2! O— -30 » »O 03CO|--^3 "v
LU O ^-»i— ov <r^-o-»"vX a^ — *3 *Orarc\i »H- *X-* ^ZZHX
lus}- mmmuj •>—<
LU 2< -r r-i a^^a a: v0 >—1— -iQi*"—3—
'»UJ--1—
_> 1- jui-u-»(j;uj^a. ;^r\j< »00|— OLUh-S:2: 0<LU-» »<Ol— i-»0C
O a:o:a:mm •—<za:oCO » r-<a^-4-——'^U-30 «-3<^000 o_h-o;<^>
I» >•>««
•»• «•I ***#I
O O^rO I<Ni
0"» 00 —'
000
5M
• »o> -^ ^m(33 • -5 -» -«• «^ -» -»w
O — — -»
O -> -3
UJ o oQ Z Z
HOQO # LU UJ• »tr -^ -» a a<33 • -•-»-» * #
o _i—_i — -.-»w_n- -»in mma>—q. incsi r-r-
> i a. i . —<n • _ • •
lu oio in t i mo I
_jLnm »o • <m I o I*- i ©mI «0 *-4 »rH »o «in to »oX3 • —..-t—^ q • fHf>- O **-*
3 U>—-O I-tw I ^twO
» OOOH o——o o—•— t—
—
i
^<JjO hOO r-iooo«» -» _l#<<h- wjjQ -—_l_)0
>» »(js -.O 3-5-»-»0 r-l^r-|^^ 0## — 0##03 • '-•O Z——*-»{J> U.U.U.U.U. _J-*~»0 —»-»-» » -J— -» -J~»-» _»-»-*.—- 3 —Z »X-5->-^ ##### <-*.-* • <^.-»
O
<—. <-^— <—-»3I——* -JH-—-»o -»inininaoO-»# "J-JO -#T5 • --# T"V*« #->->—# "S "5 «»
<h-z c^—»t— :*:^ « _jc\ir*-crocMn-^«-.w • in-^—— i—oin-»——ao—»——o*-»—«-^
# o-?o »>x i t/>ooo o » • • • •cNj-j^Ciit—ONn^^o • o-j^:£o->:*£:^o ->*:*:-5# _lO— 2r-<l— H^vN, »0 0000002T—uOoOO »Z—1/)00 iOZ-o0i/>:z —»oOo02T—»o0o0—•«. moo u__ix o ii n —ooi— z————' 'Xw »o «>x>»>%in n »xv.>^ »xn.>s »xs\x
• • #ll,i-i q:_j-»_j . lOouj-xxxxxihoom n -51—ooNtfni-oo->i-oo")Hoo->330>-t# LL Z _)"—•-»<-• • || Z>h- 1—!•—••—•<—«»—•—— J— • • C\|in«— I— • iCfh-—h • •«-»l— • •<—H • «C0
^ » • -™._ —^ —»3 I I -^-^Z<I0_LLU.lLU_X I r*HO(\JX I —H^-H-»3X I .-I^X I i-ti-tX I »-l^HC0
x -^f)H 11 i-ioari—»-jjNtqi-i«<^ h-i»-it~ 11 1 1 1—31— 11 1 1 ooi— »— (11 1 1— n 1 11— 11 1 1 »1— 11 11 ——* 11 <-*
11 11 «-.— t—-J 11 11 11 11 11 11 in——'tot— " in-"--w 11 in—— 11 ao—— 11 cr<-—
o
-i— clk-ilu-} -»-»33zll in in in coo in r\i 11 h —ooinr- 11 no. ino n 11 coo 11 11 00 11 11 —u. in •—1 11 — z> o _j_ii— h-o 11 r\jr«-ooo(\j3intno. NQiinin*-i a*3imno3coaoo3000JumNH^zrj^iTiQ «-wa)^oHzzzzzaK'M(N>H orh-r^r^. 31— o*tj>ah-cr>o>(JH o^o^t—
(\J lOU-UZ^o 1_*<J— LL, (J<~# <-»<-» U<J C_»(_# UCJ>-<(_ »cj-4 |_—i 1—h— u. i—h- I—I— I— I— I— I— I— f-cc003 Z <</!•-« <00 <i>0 <o0 <</) <002-I- O OOO - O OQX
- U\m
—» —
.
-53-> -> •*» •.
** ^ >-)-•
Z-*z z UJ-UJ UJ 03u # »# # •**.^
-^~» -,, -«, -•Ornin in 00 00 OO—o>o OCT O »3
•• • • •** » t -» »o ••
mo 1 COO 1 OO 1 U"»
o> 1 1 O IOIM
• • •0 • •O «3O »«H •—
1
O ••-1 *1 r-(— 1
-^-«I^—
.
o«— 0*-^ O—•— 0J• O'J) •OLD •JO-nOQ HOQ -H003— -I-J — -I-J >-_i_J »o<< o<< o<<-»a## o# # o##-i
# * #
^ LA
o r-- in-* o
55
-J- in-^ *^Of Of\— \—oO m» u* ~.QS
-» O 4-0m t— ~a>.— 00 CBh-C* «» h» -
h- ao •aoc/> O —O•» 0/ roo»
0* m H- —I—
V* tM 00 O •a a 1 f-mm t— LH O
'JO 00 0* mc?cr to a (N^Of —
.
1—to <M 00 t— -*
\T\ —
•
•» •ON0> a> -^ -»—a -»l— (MOT
Wt rOoO -_. ^t—-^ * » 3 —ON0O-» 1— I—*^-— LL*H oo-•» ».CQ »Os*-— *.ro—.—.ro•» fHOT •^ •HQI *
-» •4- aoco*-t—cocorgoo —U.O -u.* »-^» O-4-l—m^t(JLOO h-<-»—»I*-iH•.xo i-O •.^Qf
in •*-4«•« *> XCT*H-Xr--x «»>omo » »--oUH<)»-r*--— sO—
—
•» «-»—ooh-— r-t——
«
h-UJt— H-<UJ'-<r*- <i \— oo ( o 2: h-m 2: tuw ac>-< • •»!i>->|—CCO(jac(X-»-»i_ia: *ozz*02inNu.i-»u.«a:
—. LL -——
•
vO »-=>»o OCJ — Zh-
oooin
ao—zo•ooma:—
a 00 1/)
COGO
o
Qa» uujzi- oq:lu
OO
—00 2i-oa »a:mz2'-io •> ~o II
UJwQi »zt<2:-«o—•< 11 >r1— cc0-^"LUi—«0
c£_jluOcq<i— coZ>LU2t00 ct:—
O
a
Qw
o -*
>-> z —
•
I—» COO— «*o II
< <z1——•*:
11 a: »o u«-«
-»LUOO — LU
~-2T0O <ZCQi—1 O 1—
<
H-_Jir\ 1—
u<oOOQ
u_>zaza:
^i—QOOiULIo
<<
UJX
LUI—
oo
-4-
<c«;
*-
<
oLUXo
< »
•> »
rsjcc
»_<-51-
O »
000
X^-5— *:o<oocr: 3a -z a<— a:
000—1
r-i » 1—
t
UJ-H ||
zx >-<
—1 cc1— >tlu oo#o oO—JLUOr-):<»- 11
COLUZOO
ood 7
1 <— cc
QC
^°iI —a:•~a: *
X + LULU_1Z
-^ +1—1—+-OO—O*-* • • II 3E
II X II II UJOO H-lctZ II
—iCCh- 1—h- O.
o
oOQOOo m-»or-lh-O—O H-OOO
• tooI «o—Q.I-00—_J^ •
00 • •ftlCQi(i|— »LU<OOHZ0£II LU »oi—h-^:xo • 11 11
uu i-<u--ja
XLUU.U.O—' •—••-»
in
o 00inn 000
56
Q.XLU
+
ZSLUZt—
I
O
m^- o< —cc —
<o » t-
in —i «t(NXLU
I— Lumo^»h--JZ -»•— II UJZ
lj— >— (_ilu^ -» ZJ ex.
O II II h-l-SI^ZZ}-J a: -tct— i-ih-Q(-h-ooro^Hiuz
O-SLLOO^CtLUo
LL
LU
X
3a.z:
ao
« -»» or—
*
cx<•* aC
<t l<—oca.i x
a:*
<I
- OS_5 OLULU -»ZZ OhH • I
-2-IO2TLU • •
ozar^Oh-LU—-
»
O LU •*
I—* >——"-»U-l— II ex
Z<u_XttOLUi-tO-tU_Q£ 0<
Qd
I
H-
ai a.xo x
lu «3:uj+ r-tLU#
#~»ILU
^JOZ<LU •(—<X2-H I
I I
—-o<-|OiO.OONX •-J"-'LU—l<~»
— * #oluqc:qc<Z# * I
h->t^—I <K1—Occcccc• I ##wQ. •<!—'XfNia:*LU I I
in* <—«-•OQ-Q.o »xx
wOOLULUI I+ +«•»•««
cC#(M
aCI
a.
X
cc
#
<cC
a.xLU
<cc+
<a:
mfM
CXZa—cc
II h-U03IUJZOOCXLUo
I oI o
XH-
Z3coi—
<
cct—00t—
t
Q
<t—CO
ooLUII-
LUK»
a
i->f-<
< »
-<r^tcC
< »a:—•oooZ-4LUwQOZ3LU 3OC3 »a: « -4-
z~» <-O CC^O Q3oOf-t »o•~—-»coa:X^OtQZ—oOO * "iI— *r-l<00
•-•OX « »ZLUr-it— »LU—
I
Z—<<<-» IIMX »</) •-«
(— Ct QC-J^txaJLuci(_># cc# (jog
aC—i ••-JLU'-^
cd<qc:<h--jluqcujzo
cc<-»
LU00
aaujQ_iII CD
"1 II
cc<.Quo
*
QOQ•a •
I <N—^. I I
QQ-CQ•XCQ
(NJIUV.
•^«.QrgO •
* twcOrO'-CQ + *
W-.QQI ^*—co>to*<•<Q
cm a:*
^l a
CM-* t
*O-r0#X I
<LU—<oa— I x-*«—Olu<-QQ— 00* « |
CD | -%,H-»* o—'—>tO<fttc0< *#—CQq:<m*<-'Q--.000
i«•<
i a>--»00O—
I
Q.OJI QU
X#Q • I
LU-4-Q—4-»
-»+ q:-i^-<
^.00 I —.'J 00X I—N.CUO II
<—oa-o#_J —LUQXO^Q *-i
_J »LU •<— *—
l_) || || —CJ-» ZII <C0 || I CQ-»LUCQ<CDi-"«' —.Q
CL>}-—X<<LU0i<oas**«
—
x
Xh-
OO
X_Dh-ZI—M<h-Z
o
om
O-tOOQOrMOO
rOLn
<j>u><^> uuu
57
I
X
w JC "5>»LLI —->o^o\
—»^» ^^Qi'N.QiN,.3C>H O *Z »2 •o aim »r0 »r0CC ^ • _i *,_i ,
z r*- ii r- ii r*-
» » i-4LL <-iLL'—tLL^-» ii in «in »LnII X i_i-».-i-»,-i
•» »nl | 1M H »
x X—O>—
t
w t-f-z:-,— * ^—V-^-LUXx» OOX<LUQ—
m>< vu- oo» r*-»(NI—< (Nl ••<%) «*\j »
\^J »* •• 4J •—' 4J —» -4J —
«
LU< HJJ<m<LU<o:
•—iQ^LL,'—"QC^-hQI—(QCh-Q
3U>-HJtUL3LL3EU.a:UJ
Lf\
(Nl (Nl (Nl (Nl
58
LIST OF EEFERENCES
1. J.C. Peir and C.A. Cornell; Spatial and TemporalVariatilitv of live Loads, Jour. Structural Div. ASCE99 ST5 (1973) pp 903-922.
2. Y.K- »Jen; Statistical Combination of Extreme Loads,Jour Structural Div, ASCE, 103, ST5, (1977) pp1^7-9-TU?3T
3. H.T. Pearce and Y.K. Wen; A Method for The Combinationof Stochastic Time Varying load's Effect's STructUraTR"eseafcE S~er ies No 5(77, DTLT=^HT3=B3- 2 1 , Ci vi 1Engineering Studies, University of Illinois,Urruna, Illinois, June 1983.
H. D.P. Gaver and P. A. Jacobs On Combinations of RandomLoads, SIAM Jour Applied Hath vol 40, No. 3, June 1981.
5. P. A. Jacobs Eirst-Passage Times for Combination ofRandom Loads, Ib preparation.
6. W. "Feller An Introduction to Probability Theory andIts ^plications, volume 2, second
-ecTTtTon, J~o~En tfilev
anl 5~cn~Tnc, TTew York 1971.
i. TJ . Eudin Principles of Mathematical Analysis , Thirdedition, McGraw-Hill, New York", T9"7F.
8. M.S. Pazaraa and CM. Shetty Nonlinear Programming,John Wiley and Son Inc,New York T9"7"9~.
9. F.J. Conover Practical NonDarametric Statistics, JohnT7iley and Son Inc, New York"~T98~0".
59
INITIAL DISTRIBUTION LIST
No. Copies
1. Library, Code 0142 2Naval Postgraduate SchoolMonterey, Califonia,93943
2. Professor P. A. Jacobs, Code 55JC 2Department of Operation ResearchNaval Postgraduate SchoolMonterey, California, 93943
3. MA J Noh, Jang Kat 3Department or Operation ResearchCenter of Air ForceSeoul Korea
4
.
Defense Technical Information Center 2
Cameron StationAlexandria, Virginia 22314
60
1 3 3
101*75
Thesis
c.l
Thesis
c.l
NohA simulation study of
models for combinationsof random loads.
21d*75
NohA simulation study of
models for combinationsof random loads.
