... t
0ifs>t.
17
Then
x
0
= −
ˆ
t
0
X
1
(s)N
˜
α(s) ds,
and hence x
0
∈C(
ˆ
t). Now let 0 ≤ λ ≤ 1, and observe
λx
0
+ (1 λ)ˆx
0
= −
ˆ
t
0
X
1
(s)N(λ
˜
α(s)+ (1 λ)
ˆ
α(s)) ds.
Therefore λx
0
+ (1 λ)ˆx
0
∈C(
ˆ
t) ... means that there exists b = 0 such
that b ·x
0
≤ 0 for all x
0
∈C(t).
Choose any x
0
∈C(t). Then
x
0
= −
t
0
X
1
(s)Nα(s) ds
for some...
... something more than a feudal
lord. The kings were destined to get the upper hand before many centuries in England,
France, and Spain, and finally in Italy and Germany, and to destroy the castles ... landowners were held together
by feudalism. One who had land to spare granted a portion of it to another person on
condition that the one receiving the land should swear to be true...
... being
between 50 km s
1
and 10 0 km s
1
per million parsecs. That is, a galaxy
which is 10 0 million parsecs distant has a velocity away from us of
500 0– 10 0 00 km s
1
. For a value of Hubble’s constant ... R(t)
meets the t-axis at T at an angle
␣
, then
tan
␣
ϭPN/NT ϭR(t
0
), (1. 5)
1
2
1
2
1
2
8 Some basic concepts
TLFeBOOK
so that
NTϭPN/R(t
0
)ϭR(t
0
)/R(t
0
)...