... gcd
p,q
(P
∗
,R
∗
) and gcd
p,q
(Q
∗
,
j
R
∗
)=1for all j ≥ 1,
and
(b) let a
x
, b
x
, a
y
,andb
y
denote the coefficients of the lowest occurring powers of x and
y in A
∗
(x, 0), B
∗
(x, 0), A
∗
(0,y),andB
∗
(0,y), ... set of all integers, and the set of all non-negative integers. Let p, q, x,
and y be fixed indeterminates. Assume K = L(κ
1
, ,κ
n
) to be the field of ration...
... total number of returns in Dyck paths of
length 2n is equal to
3
2n+1
2n+1
n−1
. Each tunnel of length 2 and positive height is just the
connection line of a high peak.(Ahigh peak of a Dyck ... the number of diagram
squares of rank at least m − 2. In particular, π avoids all patterns of A
m
if and only if
every diagram square is of rank at most m − 3.
the electroni...
... f'mite set of symbols, so there is
only a finite number of strings of given length L,
and it has a finite number of rules, so there is only
a finite number of possible parse trees of given
depth ... the set
of lists s((Ao, An,B)) such that (Ao, An) ~ D n,
(A',B) ~ D t, and s is the most general unifier of
A n and A' (after suitable renaming of varia...
... movement of the Au ions is shor-
tened, and the formation of 0-D GNSs instead of 1-D
GNSs becomes dominant. By optimizin g the heating and
UV irradiation condition of our method, 1-D and 0-D
GNSs ... resonance and third-order nonlinear optical properties
of gold nanorods. Nanotechnology 2011, 22:275203.
Figure 5 DR spectra of Au
3+
ion-adsorbed 20Ti and 0Ti and of 1-...