Journal of Kufa for Mathematics and Computer

In this paper, we give an alternate proof to the main theorem of [1], then generalize the result to cover arbitrary functions, and we study the separation of any function with three variables. Also, we introduce a way to factorize such function.

In this work we study quasi-confluent mappings, where we the relation between these mappings and confluent mappings. Also, we study some operations on quasi-confluent mappings, such as: the pullback, factrization, composition and product of quasi-confluent mappings .

We consider a single machine scheduling problem to minimize a multiple objective function; sum of earliness, tardiness and completion time. As this problem is complete NP-hard we propose a branch and bound algorithm to obtain an optimal solution. The implementation of optimizing algorithms dose seen to be promising but it need longer time. Thus we tackle the problem with local search methods: descent method, simulated annealing and threshold acceptance. The performance of these heuristic methods is evaluated on a large set of test problems, and the results are also compared with these obtained by genetic algorithm and hybrid method which is combining the simulated annealing with the genetic algorithm. The best results are obtained with the hybrid method. We solved the problem optimality with up to 35 jobs and approximately with up to 150000 jobs.

In this paper, we introduce the concept of Banach Algebra valued measure, several properties of this
measure are proved.

Most database systems initially concentrated on handling typical business data such as: Columns of
numbers, short text, and dates. With the advent of powerful and affordable multimedia computers, people
increasingly need databases to store more complex objects. Typical objects include graphics, sound, and video
clips. For some applications, like geographic Information Systems(GIS) and computer-aided design (CAD),
developers need the ability to define their own objects.
Storing objects involves two aspects: storing data for their properties and storing and activating their
methods. The first part- storing properties – is relatively easy. In relational database, the properties becomes
columns. Relational databases can be adapted to handle objects. On of main components is the ability to define
new data types. These data types are treated as objects, and they can inherit properties from other data types.
Many commercial applications are created using OO methodologies. Given that several object-oriented
applications might need to share the same data, we describe how such applications can interoperate with each
other. By exposing the internal object properties and methods, the developers can use the applications to create
the complex integrated business applications. The applications can use all the features of a spreadsheet, word
processors, or graphics packages.
This technology also provides function as well as data together so that the data can be manipulated by
the given function. we show that how the data is more secure in object-oriented database than in relational
database and also why do we migrate from RDBMS into OODBMS.
In this paper, we describe the major characteristics and requirements of object-oriented applications and
how they may affect the choice of a system and method for making objects persistent in that application

The problem of estimation of variance components occurs in many areas of research. This paper is
devoted to study the comparison between Minimum Norm Quadratic Unbiased Estimator (MINQUE) and
Ordinary Least Square Estimator (OLSE) of 2 s in the Gauss Markoff Model{ } Y X V
2
, b, s , under mean
square errors criterion, where the model matrix X need not have full rank and the dispersion matrix V can be
singular.
A necessary and sufficient condition is obtained for that MINQUE is superior to simple estimator, in
particular, a simple sufficient condition is that the degree of freedom of errors is equal to or greater than 4.39

In this paper, we introduce and study compact-F and Lindel ..
o f -C Spaces .Compact-F space is a topological space in which every compact subset is finite, Lindel o f-C Space is a topological space in which every Lindel o f subsets is countable several properties of these spaces are proved.

In this paper, we review here some of the ideas we have encountered in Orlicz function and define S*Orlicz lattice. We have proved that S*-Orlicz space (X, ||.||F) is a normed S* -Vector Lattice, complete and therefore, it's a Banach S*-Vector Lattice.

We Obtain a direct theorem for the simultaneous approximation of 3-monotone functions in Lp
by splines in Lp
.

For fixed positive integer n³3 ,let Dn be the dihedral group, Dnh= Dn ÏC2 and cf(Dnh,Z) be the abelian
group of Z-valued class functions of the group Dnh .The intersection of cf(Dnh,Z) with the group of all
generalized characters of Dnh , R(Dnh) is a normal subgroup of cf(Dnh,Z) denoted by R (Dnh),then
cf(Dnh,Z)/ R (Dnh) is a finite abelian factor group which is denoted by K(Dnh).
In this paper ,we determine the cyclic decomposition of the finite abelian factor group cf(Dnh,Z)/R(Dnh)
when n is an odd number, we find that the cyclic decomposition of K(Dnh) depends on the elementary divisor of
n ,if n= p 1
1
a
.p
2
2
a
..p
m
m
a
where p1
,p 2
,…, p m are distinct primes and
1
a ,a2
,..,am
are positive integers, then ;
K(Dnh)=
2
=1
Å
i
K(Dn)
( )( ) ( ) 1 1 1 2
1
1+ × 2 + + -
=
Å
m
i
a a L a
C2
Å
K(C4). And we find the rational valued
characters table of the group Dnh.

In this paper, two separately methods were suggested for coding information .The first method was
introduced using the directness of symmetric matrices .The contraction function was used for introducing the
second method .For more complexity the presented two methods were gathered in one method . And it is proved
that the direct product preserves the property of Hermitian positive definite matrices .

Under the multivariate linear model{ } Y , Xb ,å ÄV , A number of characterization of the distribution of
Xi
have been made based on the properties of the statistics Y1
andY2
when Y1
andY2
be two linear functions
defined on 1 R as follows
n Xn Y = a X + ....+ a 1 1 1
and n X n Y = b X + .....+ b 2 1 1
. Generalizations of these
problems to the multivariate case have been made by several authors by extending the techniques used in the
univariate case. In my paper I shall consider some other generalization, which possibly require development of
new techniques ,if 1 2 X , X be independent and identically distributed p-vector r.v.,
s such that
( \ ) 0 E X1 - AX2 X1 + B¢X2 = ,where A and B are nonsingular matrices. In special case when -1 A = B , A
is symmetric and the egen values do not take values ±1. Under these conditions that X1
has an m.n.d.
in the present paper we shall consider a few other cases.

In 1995 Kopotun [4], introduced a paper on k -monotone polynomial and spline approximation in LP
,
0 < p < ¥ quasi norm . In this paper, we discuss the errors of approximation of k -monotone function by k -
monotone interpolation . It turns out that any two k -monotone functions f and g , whose graphs intersect
each other at certain ( sufficiently many ) points in [ ] a,b , have to be "close" to each other in the sense that
P
f - g , has to be small .

The main aim of this paper is to study new class of continuous function is called ac – continuous function.
for this aim , the nation of a - open and pre – open sets and a - compact space are introduced. and we shall study
their relation ship between ac – continuous and pc – continuous function .