Volume
7, No.
2, June
2014
Articles 


Various Error Estimations for Several Newton–Cotes Quadrature Formulae in Terms of at Most First Derivative and Applications in Numerical Integration
Error estimates for midpoint, trapezoid, Simpson’s, Maclaurin’s, 3/8Simpson’s and Boole’s type rules are obtained. Some related inequalities of Ostrowski’s type are pointed out. These results are obtained for mappings of bounded variation, Lipschitzian, and absolutely continuous mappings whose first derivatives are belong to Lp[a,b] (1≤p≤∞) Applications to numerical integration are provided. 

M. W. Alomari
S. S. Dragomir
JJMS, 2014,
7(2), 89108

Monotonic Analysis: Some Results of Increasing and Positively Homogeneous Functions
The theory of increasing and positively homogeneous (IPH) functions defined on a convex cone in a topological vector space X, is well developed. In this article, we present necessary and sufficient conditions for the minimum of the difference of strictly IPH functions defined on X. We study convergence of sequences of increasing positively homogeneous (IPH) functions defined on X. 

H. Mazaheri
Z. Golinejad
JJMS, 2014,
7(2), 109118

Related
Monotonic
Functions
We
continue
the
study of
related
sets
introduced
by Prof.
Min and
generalize
some of
his
results. 

M. Sasirekha
JJMS,
2014, 7(2),
119130

Central
Idempotent
of Rings
In this
paper, we
find several
necessary
conditions
for the
idempotents
of a ring
R to be
central (for
example: if
eU_{R}
=U_{R}
e
for every
idempotent e
of R
then the
idempotents
of R
are central,
where
U_{R}
is the set
of units in
R).
We present
some several
properties
of a ring
whose
idempotents
are central
(for
instance: If
I_{R}ÍC_{R}
then reg R =
S.cl_{R}
where reg
R is the
set of
regular
elements in
R and
S.cl is the
set of
strongly
clean
element in
R). 

MohamedKheir
Ahmad
Sumyyah AlHijjawi
JJMS,
2014, 7(2),
131145

Empirical
Bayes
Estimates
of
Rayleigh
Distribution
with
Ewmel
and
Logarithmic
Loss
Functions
for
Censored
Samples
In this
paper,
empirical
Bayes
estimates
of
reliability
performances
are
derived
when the
data are
progressively
Type II
censored
from a
Rayleigh
distribution.
These
estimates
are
derived
under
exponentially
weighted
minimum
expected
loss
(EWMEL)
and
logarithmic
loss
functions,
and
compared
with the
corresponding
maximum
likelihood
estimates
in terms
of
absolute
bias and
estimated
risk. A
real
data set
is
presented
to
illustrate
the
proposed
estimation
method,
and a
Monte
Carlo
simulation
study is
carried
out to
investigate
the
accuracy
of
derived
estimates.
The
study
shows
that the
empirical
Bayesian
estimation
outperforms
the
maximum
likelihood
estimation.


D. R. Barot
M. N. Patel
JJMS,
2014, 7(2),
147170

