Journal of Kufa for Mathematics and Computer

In this paper, we prove that the general form of Artin's characters table of the group (Q2m Cp ) such that
Q2m be the Quaternion group of order 4m when m is an odd number and Cp be the cyclic group of order p
when p is prime number and (Q2m×Cp) be direct product of Q2m and Cp such that
(Q2m Cp ) = {(q,c):q Q2m ,c Cp} and |Q2m×Cp|=|Q2m|.|Cp|=4m.p=4pm.
This table which depends on Artin's characters table of a quaternion group of order 4m when m is an odd
number. which is denoted by Ar(Q2m Cp ).

An attempt to quantify the spectral response of the polychromatic light sources and drinking
water samples has been presented in this research. This had been executed by an objective methods of image
quality assessment, in which the criteria of error visibility (differences) between images had been applied
theoretically and practically. The theoretical part had been presented here by image quality assessment
which gave results match with that of the practical part resulted by lab investigation. Otherwise and in spite
of its differences in physical and chemical properties, samples of drinking water with their existence
percentage didn't make any variation in the spectrum of polychromatic light sources and hence the spectrum
of the light sources remains unchanged.

“In this paper we disperse the outcome of threshold functions for designate feed forward neural
network for solution partial differential equations ”. “We utility a multi-layer network having one hidden layer with
7 hidden units (neurons) and one linear output unit with different of threshold function of each unit are logsig ,
tansig, purelin, tribas and hardlim and use Levenberg – Marquardt (trainlm) training algorithmic rule”. Finally
the terminate of numerical experience are compare to with the true solution in illustrative examples to ratify the
precision and effectiveness of the immediate plan.

The notion of dual Rickart modules has been studied lately. In this article, we continue
investigate and study several properties of closed dual Rickart modules which explain by Ghawi Th.Y. as a
proper generalization the idea of the dual Rickart modules and as a dual concept of closed Rickart
modules. A right R-module M is called closed dual Rickart if, for each , is a closed
sub module of M . For a module M, we verify that M is closed dual Rickart and closed simple if and only if
M is coquasi-Dedekind and Extending . We also establish that if, and are closed simple modules such
that is closed dual Rickart and is projective, then either
or ".
Furthermore, "we give a counter example to show that the direct sums of modules is not closed under closed
dual Rickart"."We also give a necessity station for a finite direct sum of closed dual Rickart modules to be
closed dual Rickart". Other results are provided in this work. Examples to illustrate some results and
converses are given.

The main purpose of this paper is to find Artin's characters table of the group (Q2m×C4)when
m=2h
, h∈Z
+
, which is denoted by Ar(Q2m ×C4) where Q2m is denoted to Quaternion group and C4 is the
cyclic group of order 4 .Moreover we have found The rational valued characters table and the cyclic
decomposition of Artin's cokernel AC(Q2m ×C4) when m=2h
, h∈Z+

The one-dimensional Volterra Integro-Differential Equations of the second kind associated with local
fractional derivative operators are investigated. Analytical solutions are obtained by using the local fractional
variational Iteration method (LFVIM). The method in general is easy to implement and yields good results.
Illustrative examples are included to demonstrate the validity and applicability of the new technique.