IRAOI JOURNAL OF STATISTICAL SCIENCES

This paper sheds light on the theory of chaos, which is one of the latest
mathematical theories. Some aspects of the scientific, applied and
philosophical fields related to this theory are studied, then focus the
spotlight on the solar system as one of the most important natural
systems. The chaotic property is studied for three particulate
mathematical models fitted the time series of the sunspots, one linear and
two non linear. The long-term behavior of these models is examined . It
is clear that one of the two non linear models gives similar behavior to the
behavior of real data of sunspots. The behavior of this model has chaotic
nature, which indicates that the solar system is a chaotic system. It also
proposed a computer algorithm which shows the possibility of
transmission of a phenomenon from the state of semi-nothingness, to the
chaotic state, and then to the order and stability.

In this paper, we concentrate on two cases of fuzzy linear programming
problems (FLPP): LPP with coefficient of objective function and coefficient
of available resources and constraint are trapezoidal and triangular of fuzzy
numbers respectively. Though by using a - cut ,fuzzy numbers (fuzzy
triangular and fuzzy trapezoidal ) can be transformed into interval numbers
and by taking one type of non-linear membership function this meant
logistic function, we propose here the "modified S-curve function by simplex
method

In this paper, a new almost unbiased estimator is proposed under stochastic linear
restrictions model as alternative to mixed estimator. The performance of the proposed
estimator compared to mixed estimator is examined using the matrix mean squared
errors

The methods for solving nonlinear multi-objective optimization are
divided into three major categories: methods with apriori articulation of
preferences, methods with a posteriori articulation of preferences, and
methods with no articulation of preferences. Really there is no single
approach is superior. In this paper, a combination between two well
known approaches has been used to solve multi-objective GP problems
having negative degree of difficulty. First, we use an alternative
procedure for converting GP problem having negative degree of difficulty
to positive degree of difficulty; second we proposed to discuss all
available cases for any number of multi-objective in GP problems using
Lexicographic method. This avoids the difficulty of non-differentiability
of the dual objective function in the classical methods

This paper deals with Reliability of Acceptance Sampling Plan
(RASP) which differs from ordinary sampling plan for a static quality
characteristic,since it involves a non-normal fail time distribution and
censored data.The plans consist of the optimal sample size and the critical
number of failures which satisfy the consumer and producer risks are
determined for a given censoring time.the distribution of life time is Gamma G(θ,γ ) where the shape parameter (γ ) is known ,plans are
tabulated for selected combination of consumer and producer risks and
parameter values are achieved by using matlab program written for this
purpose.

In this paper we studied and found the stability conditions of the
(AEXPAR) model by using a dynamical approach and by adopting the
linear approximation technique.

In this paper, we study the statistical and chaotically analysis for
the real observations represented by the observations of rainy day falling
on Mosul city , diagnose its behavior using some measurements and
indicators of statistics and chaos that are applied directly on the time
series data by using a new binary technical test, the 0-1 test for chaos, to
identify some of the statistical and chaotic characteristics features for the real observations using the techniques and computer simulations
represented by time series curve, State-Space Diagram. Periodicity is
identified by the spectral analysis, check independence is based on
the correlation integral and free statistics by using the statistical
indicator BDS, and that supports the diagnosis of conduct for these
observations. In this study, real observations for the years
1994-2000. Show, through this paper, that the time series of rainfall in the
city of Mosul is not independent and its behavior is non-periodic, chaotic
and irregular, this can not predict its behavior in the long time.

The aim of this paper is to give a characterization between the
external and internal sets, and some relation between the galaxies and
monads, according to this paper we obtain the following results :
v A set is galaxy iff there exists a strictly increasing sequence of
internal sets such that .Also A set is monad iff there exists a strictly decreasing
sequence of internal sets such that .
v If is a galaxy and is a monad such that , then there
exists an internal set such that G Ì I Ì H .
v A monad is not galaxy.
v If is a monad and is a galaxy, the set of all internal functions
f : G ® H such that f (H ) = G is a monad)

In this paper we study a numerical solution of coupled BBM systems of
Boussinesq type, which describes approximately the two ways propagation of surface
wave in a uniform horizontal channel of length l filled in its undisturbed depth h. This
paper is devoted to drive the matrix algebraic equation for the one-dimensional
nonlinear BBM system which is obtaining from using the implicit finite difference
method. The convergence analysis of the solution is proved. Numerical experiments
are presented with a variety of initial conditions describing the generation and
evolution of such waves, and their interactions.

The research objective adoption idea came to build and study the state
space models to identify the reasons of epilepsy on basis of the brain waves
frequency, where two models have been built, the first of which is
concentrated on building state space models to estimate epilepsy seizure
whereas the second is concentrated on building the state space models to
identify the reason of the disease via displaying a statistical procedure
programmed on the computer to facilitate the specialist doctors task to stand
on the specific reasons of each state so as to enable them to give the patients
the correct medicine.

In the present paper, we define a new family of summation-integral Beta
operators to approximate a class of unbounded continuous functions of polynomial
growth , for some and then we estimate the rate of convergence for this
family for functions have derivatives of bounded variation

In this paper, an operational matrix of integrations based on the
Haar wavelet method is applied for finding numerical solution of nonlinear third-order korteweg-de Vries-Burger's equation, we compared this
numerical results with the exact solution. The accuracy of the obtained
solutions is quite high even if the number of calculation points is small,
by increasing the number of collocation points the error of the solution
rapidly decreases as shown by solving an example. We have been
reduced the boundary conditions in the solution by using the finite
differences method with respect to time. Also we have reduced the order
boundary conditions used in the numerical solution by using the boundary
condition at x=L instead of the derivatives of order two with respect to
space.

Modified (r, k) class ridge regression (MCRR) which includes unbiased ridge
regression (URR), (r, k) class, principal components regression (PCR) and the
ordinary least squares (OLS) estimators is proposed in regression analysis, to
overcome the problem of multicollinearity. In this paper, we derive the necessary and
sufficient conditions for the superiority of the MCRR estimator over each of these
estimators under the Mahalanobis loss function by the average loss criterion. Then,
we compare these estimators with each other using the same criterion. Finally, a
numerical example is done to illustrate the theoretical results.

In this paper we introduce a subclass of multivalent harmonic meromorphic functions defined
in the exterior of the unit disk by using generalize hypergeometric functions. We derived
sufficient coefficient conditions and shown to be also necessary for this subclass by putting
certain restrictions on the coefficients, distortion theorem, extreme points and other
interesting results are also investigated.

In this paper, some exact solutions for the convection–diffusion–reaction equation in
two dimensions and a nonlinear system of partial differential equations are formally derived
by using the first integral method, which are based on the theory of commutative algebra

In this paper we study rightidempotent reflexive ring whose simple singular
right R-module isYJ-injective, we prove that this type of ring is right weakly
regular ring, we show that if R is N duo or NCI ring and R is right idempotent
reflexive ring whose every simple singular right R-module is YJ-injective then R is
reduced weakly regular ring

In this paper, a new Spectral Conjugate Gradient (SCG) method
for solving unconstrained optimization problems; based on inexact line
searches is investigated. The search directions of the new CG method are
always sufficient descent. The global convergence property of the
proposed method has been proved. Finally, we have presented some
numerical results to examine the efficiency of the proposed method.

Most of the time the researcher confronts a decrease in the experimental
units required when applying a certain design, this problem appears
especially when conducting the factorial experiments which mostly need
great numbers of experimental units, to overcome the decrease of the
experimental units three incomplete block designs have been used in
order to point out which one is best and to know as well the extent of the influence of a number of experimental units on the results of statistical
analysis.
A factorial experiment 23
has been conducted on the dry weight of lentil
seeds (mg/10 plants) and the experiment factors adopted are: the method
of plantation, the locran herbicide and the soil moisture. The experiment
of the randomized complete block design has been applied in seven
blocks and considered as comparative experiment, from this experiment,
the following incomplete block designs have been created were: the
balanced incomplete block design, complete confounding and partial
confounding.

Several learning algorithms for feed-forward (FFN) neural networks
have been developed, many of these algorithms are based on the gradient
descent algorithm well-known in optimization theory which have poor
performance in practical applications. In this paper we modify the PolakRibier conjugate gradient method to train feed forward neural network.
Our modification is based on the secant equation (Quasi-Newton
condition). The suggested algorithm is tested on some well known test
problems and compared with other algorithms in this field

In this paper, we have discussed and investigated an extended PR-CG method
which uses function and gradient values. The new method involves the extended CGmethods and have the sufficient descent and globally convergence properties under
certain conditions. We have got some important numerical results by improving a
standard computer program compared with Wu and Chen (2010) method in this field.

Al-Sanjary (2001) mentioned the values of mean and standard
deviation of the power of hydrogen (pH) and concentration of carbon
dioxide (CO2) in the water of Tigris river in Mosul city, the study was
applied over five locations during ten months. This information were used
to simulate thirty values of each location during each month. The simulated
data were used to compare some statistical analyses which are: analysis of
variance followed by Student Newman Keules Test to compare between the means, factor analysis with axes rotation and the simple correlation
coefficient. The results are presented in figures and charts to simplify the
visual comparisons. The statistical analyses approach to the same
conclusions. It was concluded that the power of pH and the concentration
of CO2 were highly effective in the region of Danadan, also the two
variables were increasing in September. However the regions affected the
two variables more than that months did.

This paper presents the development and implementation of a new
unconstrained optimization method; based on the inexact line searches.
Our new proposed Conjugate Gradient (CG) method always produces
descent search directions and has been shown to be a global convergence.
Our numerical results are promising in general by implementing ten
nonlinear different test functions with different dimensions.

In this paper, we present modified conjugancy coefficient for the
conjugate gradient method based on the (Liu and Storey) method to
solve non-linear programming problems. We proved the sufficient
descent and the global convergence properties for the proposed
algorithm for three cases and we get very good numerical results
especially for the large scale optimization problem.

In this paper, using algorithm models of Hidden Markov models, it has
been concluded that the possibility of recognizing the warp face and the
morph face the image real departments face on recognizing object. In
through applicability Algorithms model of Hidden Markov and allegation
with Algorithm (Beier-Neely) get through in to practicability the defining
recognizing the warp face image and the morph face image. The results of
hidden Markov models indicate that the matrix at the final iterate able to
recognize the warp face and the morph face. Programmers of all algorithm
are writhen using the language Matlab (R2008a) 7.6.0.

Conjugate Gradient (CG) methods comprise a class of unconstrained
optimization algorithms which are characterized by low memory requirements
and strong local and global convergence properties. Most of CG methods do not
always generate a descent search directions, so the descent or sufficient descent
condition is usually assumed in the analysis and implementations. By assuming a
descent and pure conjugacy conditions a new version of spectral Dai-Yuan (DY)
non-linear conjugate gradient method introduced in this article. Descent
property for the suggested method is proved and numerical tests and
comparisons with other methods for large-scale unconstrained problems are
given

This study deals with the prediction of the non-stationary spatial
stochastic process. The prediction is done by two techniques which are
regression technique (generalized least square estimation) and universal
kriging technique. As it is familiar, that the non-stationary stochastic
process has a trend (mean) as a linear or non-linear model. By this
process we can find covariance function from knowing the variogram
function and the latter is attributed to a spherical variogram model, also in
order to estimate parameters of spherical model by minimum norm
quadratic unbiased estimator which requires that the covariance function must be linear in the parameters, then changing the spherical model into
an approximated linear model by Taylor series in the linear approximation
The prediction in these two techniques is applied to real data which
represent height levels of ground water of 47 wells with their regional
coordinates in Sinjar district in Ninevah Governorate in Iraq. The results
were so encouraging where we show the approximation between the
predictive values and the real values as well as computing the variance of
prediction in these two techniques. It is shown that the prediction
variance of universal kringing is less than that of regression.

In this paper, based on the memoryless BFGS quasi-Newton method,
we propose a new modified Hager-Zhang (HZ) type method. An
attractive property of the proposed method is that the direction generated
by the method is always a descent direction for the objective function.
Moreover, if the exact line search is used, the new method reduces to the
ordinary HS method. Under appropriate conditions, we show that the
modified HZ method is globally convergent for convex and general
functions. Numerical results are also reported.

The training phase of a Back-Propagation (BP) network is an
unconstrained optimization problem. The goal of the training is to search
an optimal set of connection weights in the manner that the error of the
network out put can be minimized. In this paper we developed the
Classical Fletcher-Revees (CFRB) method for non-linear conjugate
gradient to the scaled conjugate gradient (SFRB say) to train the feed
forward neural network. Our development is based on the sufficient
descent property and pure conjugacy conditions. Comparative results for
(SFRB), (CFRB) and standard Back-Propagation (BP) are presented for
some test problems.

In this study, new charts were formed using Baysian technique and they
were called Baysian chart (c
2
B) , to control the average . The control chart (c
2
B)
was used and the process includes real data that involved results of test of the
asphalt concrete samples of the base layer used in the construction of new
streets. These samples were obtained from the general authority of roads and
bridges / The general directorate of roads and bridges in Nineveh province .

In this paper we proposed a new HS type conjugate gradient method by
using two kind of modification, first derived a new non-quadratic model second
using structure of the memoryless BFGS quasi-Newton method. The new proposed
method always generates a descent condition. We give a sufficient condition for
the global converges of the proposed general method. Finally, some numerical
results are also reported

Palm print biometrics technology is highest used for human identity
verification in most of security application. In this research the
automated biometric system based palmprint biometric technique is used.
The procedure of implementation is divided into two Stages (Enrollment
stage and Verification stage). Each stage is divide into three parts ,the first
part is pre-processing techniques based on image requirement and
cropping to achieve the better image for palmprint. The second part is
feature extraction based on countourlet to obtain a good coaffiention and
KL transform to have eign values that reduce the input .The third part is a
classifier using backpropagation neural network to authentication. The
automated biometric system is feasible, easiest to use, and effective in
personal authentication using palmprint features with high detection rate
(97% )

This research deals with modeling cumulative number of patients with
cancer disease in Nineveh Iraq. The method is based on classes of
Exponential Growth Models ( ) EGM s and uses the ideas of Non-Linear
Dynamic Generalized Model(NLDGM). We take three types of ) (EGM s ;
Modified exponential, Logistic and Gompertz and use the First-order
Tayler series to approximate the Non-linear model to a linear model.Also
this research, the discount factor has been explainy, and finding forecast
distribution and forecast values by using Bayesian forecasting Approach

In this research an algorithm was suggested for classifying a speaker age
to two classes: (young and old classes) based on his speech signal. The
suggested algorithm depend on a speech signal feature extraction in order
to get a compact representation for this signal and to adopte these
features in the classification process.
In this algorithm, the eigen values of the covariance matrix was adopted
as a principle parameter in the recognition between the two classes. It
was constructed from the data of the speech signal (usually one
dimension )after rearranghng it into a number (2,4,8,16,32,64) of a two
dimension square matrix array . The suggested algorithm include two
main stages:
¨ 1st stage: includes data file preparation that contains the eigen values
for a number of persons belong to both classes young and old (with
different gender), in this stage the average of these values for each class
to be calculated separately and the threshold curve(which represents the
boundary seperating between two classes) were also computed.
Second stage: in this stage the classification process was done by
comparing the curve that represents the eigen values of the speech signal,
with the threshold curve, a different number of performance parameters
are adopted in the evaluation the accuracy of the classification process.
The measured correlation value was in range of (0.9610, 0.9994 ) when
m=2 and m=64, respectively (this means whenever the number of arrays
that the speech signal constructed from it increases, the correlation
coefficient also increases) , while a clear difference can be seen with
mmse parameter. After applying the suggested algorithm on 50 persons
from both genders, the algorithm passed in applying 80% and failed in
percentage 20% of them.

In this paper, The probability distribution of the estimated stochastic
ridge factor has been found, which has been developed by adding prior
information to the sample information. These information has been represented
by the information about the parameters of multiple linear regression model
which are in the form of mixed linear model which contains the fixed and
stochastic information.