... E
k
n,χ,ζ
x
.
1.12
The purpose of this paper is to present a systemic study of some formulas of the
twisted q-extension of the generalized Euler numbers and polynomials of order k attached
to χ.
2. On the Twisted ... let us consider the twisted
h, q-extension of the generalized Euler numbers and polynomials of order k attached to...
... from the classic equation of Marchenko and we call the
equation the modified Marchenko equation. The discontinuity of the function ρx strongly
influences the structure of the fundamental equation ... equation of Marchenko and we call equation 3.14 the modified M archenko equation.
The discontinuity of the function ρx strongly influences the structure of...
... equation of Marchenko and we call equation 3.14 the modified M archenko equation.
The discontinuity of the function ρx strongly influences the structure of the fundamental
equation of the boundary ... from the classic equation of Marchenko and we call the
equation the modified Marchenko equation. The discontinuity of the function ρx strongly
influences...
... summary above,
share a common structure on the joint distributions of
their (nonzero) eigenvalues. Based on the common structure,
we then derive the marginal distributions of the ordered
eigenvalues, ... Section 2
presents the common structure of the joint eigenvalue
distributions. Based on the common structure, Section 3
derives the general expression for the ma...
... b to the perturbations on A and b. There are several methods that allow to find
good approximations of the condition number of a general square matrix.
Let C
n×n
and R
n×n
be the space of n × ... 336 .The
condition number κAAA
−1
of a nonsingular matrix A plays an important role in the
numerical solution of linear systems since it measures the sensitivity...
... bit
depends on k
− 1 random matrices. The total number of 1’s
among these g
− l bits (the Hamming weight of the vector)
is a random v ariable with a binomial distribution, and the
expected value of the ... B
(k,n)
3
=
⎛
⎜
⎜
⎜
⎝
{2,3}
rr
11
11
⎞
⎟
⎟
⎟
⎠
.
(26)
The first two rows of
B
(k,n)
1
are from the first two B
(2,2)
1
matrices. The first row, and the thir...
... Journal of Inequalities and Applications
then we know that F is analytic in U, F01, and Re fz > 0 z ∈U.ThusF is the
Carath
´
eodory function. Since the extremal function for the Carath
´
eodory ... Relevant connections of the definitions and results presented in this paper with those
obtained in several earlier works on the subject are also pointed out.
1. Intro...
... measurement of the aircraft, there is a false one.
The synthetic measurement is the mean of both. It is farther
away from the prediction than the measurement of the air-
craft, and represents ... lower bound of the
following E-Step. E-Step and M-Step are repeated until the
estimates converge. How the M-Step is done depends on the
application. PMHT is the ap...
... torsion monitoring. The method focuses on
small angle deformation detection and on online data
acquisition, in order to provide immediate identification for
nonconformities. It consists of attaching ... at the minimization of the
sum of the squares of the difference between the desired signal
and the filter output signal. When new samples of incoming
signals are r...
... be considered as a
further extension of the A
λ
r
Ω-weight.
We keep using the traditional notation.
Let Ω be a connected open subset of R
n
,lete
1
,e
2
, ,e
n
be the standard unit basis of
R
n
,andlet
l
l
R
n
... completed the proof of Theorem 3.3.
Journal of Inequalities and Applications 9
Choosing m s/αλ
3
r −1s, then m<s<t. Applying the weak r...