... y
2
for n ≥ n
0
6.1
or
y
n
< y
2
for n ≥ n
0
. 6.2
We only prove the case where 6.1 holds. The proof for the case where 6.2 holds is similar
and will be omitted. According to 6.1,forn ... α
j
< y
2
for j odd and y
2
<α
j
≤ for j even,
2 α
j
α
jk1i
,j∈{−k,−k 1, },i∈{0, 1, }.
Now, either α
j
∞ for some even j in which case the proof is complete, or α
j...
... Corporation
Advances in Difference Equations
Volume 2009, Article ID 484185, 16 pages
doi:10.1155/2009/484185
Research Article
Bounds for Certain New Integral Inequalities on
Time Scales
Wei Nian Li
1, 2
1
Department ... 2.7. The result of Theorem 2.5 holds for an arbitrary time scale. Therefore, using
Theorem 2.5, we can obtain many results for some peculiar time scales. For e...
... where α is replaced by π α for
α ∈ −π, 0 and −π α for α ∈ 0,π,andK is replaced by −K.
Before proving Theorem 3.1, we prove the following five propositions.
Proposition 3.3. For λ ∈ C, λ is ... det Iλ0. Then, for any fixed λ with
fλ2or−2, the matrix Iλ is positive semidefinite or negative semidefinite. Therefore,
for such a λ, fλ cannot vanish unless δ
j
λ0 for...
... f
1
d
m−1
d
m
≤
d
1
,
(59)
then the upper bound for the eigenvalue λ
1
(Q)givenby(34)
in Theorem 11 is tighter than that by (2). The upper bounds
for the eigenvalues λ
j
(Q), j = 2, , m −1, provided by (34)
in Theorem 11 ... that
λ
j
(
E
)
=
d
j
(22)
for j
= 1, 2, , m.ByCorollary 2,wehave
λ
1
(
S
)
= s, λ
m
(
S
)
= t, λ
j
(
S
)
= 0, for j = 2, , m −1,
(23)
where s and t are...
... the
conductor of χ
1
is not a power of p. The explicit formula given in Theorem 1.5 by Fox yielded
to derive formulas similar to that obtained by Young, but for all primitive Dirichlet character χ.
In 16, ... Publishing Corporation
Journal of Inequalities and Applications
Volume 2008, Article ID 270713, 19 pages
doi:10.1155/2008/270713
Research Article
Congruences for Genera...
... Publishing Corporation
Boundary Value Problems
Volume 2007, Article ID 27621, 17 pages
doi:10.1155/2007/27621
Research Article
Solvability for a Class of Abstract Two-Point Boundary Value
Problems ... prove that system (3.2)hasasolutionon[a,b]foranyβ
∈ [δ,2δ].
Clearly, after finitely many steps, we can prove t hat system (3.2)hasasolutionforβ
= 1.
Therefore, system (3.1) has a solution...
... Publishing Corporation
Boundary Value Problems
Volume 2008, Article ID 723828, 14 pages
doi:10.1155/2008/723828
Research Article
Solvability for Two Classes of Higher-Order
Multi-Point Boundary Value ... 2008
Recommended by Ivan Kiguradze
Using the theory of coincidence degree, we establish existence results of positive solutions for
higher-order multi-point boundary value problem...
... large, such that xt > 0fort ≥ t
1
. It follows from
1.1 that x
Δ
n
t ≤ 0fort ≥ t
1
and not eventually zero. By Lemma 2.6, we have
lim
t →∞
x
Δ
i
t
0, for 1 ≤ i ≤ n − 1,
−1
i1
x
Δ
n−i
t
> ... xt > 0 with x
Δ
n
t ≤ 0 for t ≥ t
0
and not
eventually zero. If x is bounded, then
1 lim
t →∞
x
Δ
i
t0 for 1 ≤ i ≤ n − 1,
2−1
i1
x
Δ
n−i
t > 0 for...
... low-training overhead equalizer for the
general case of frequency selective transmitter and receiver
IQ imbalance together with CFO and channel distortion
for single- input single- output (SISO) systems. ... of
size (N
× 1) where N is the number of tones. This symbol
is transformed to the time domain by an inverse discrete
Fourier transform (IDFT). A cyclic prefix (CP) of length ν
is t...
... current block is fixed. For
asearchangleintervalΔθ, block matching will be performed
for each block-rotation of nΔθ, n
∈ Z,startingfrom0
◦
within a search angle range. For example, if the search
angle ... 10
◦
/0.1
◦
= 100 rotated block matching will be
performed. For practical implementation, we choose a lower
number of rotational searches. For example the performance
of using 16 se...