Convergence prop erties of Jackson polynomials have been considered by Zugmund
[1,ch.X] in (1959) and J.Szbados [2], (p =ï‚¥) while in (1983) V.A.Popov and J.Szabados [3]
(1 ï‚£p ï‚£ ï‚¥) have proved a direct inequality for Jackson polynomials in L
p-sp ace of 2-periodic bounded Riemann integrable functions (f R) in terms of some modulus of
continuity .
In 1991 S.K.Jassim proved direct and inverse inequality for Jackson polynomials in
locally global norms (L
,p) of 2-p eriodic bounded measurable functions (f L) in terms of
suitable Peetre K-functional [4].
Now the aim of our paper is to proved direct and inverse inequalities for Jackson
polynomials

in this paper sufficient conditions of oscillation of all of nonlinear second order neutral differential eqiation and sifficient conditions for nonoscillatory soloitions to onverage to zero are obtained

In this paper, we will study and prove the existence and the uniqueness theorems
of solutions of the generalized linear integro-differential equations with unequal
fractional order of differentiation and integration by using Schauder fixed point
theorem. This type of fractional integro-differential equation may be considered as a
generalization to the other types of fractional integro-differential equations
Considered by other researchers, as well as, to the usual integro-differential
equations.

     In this paper, the oscillation of a Hematopoiesis model in both cases delay and non-delay are discussed. The place and are continuous pstive -rdic functions. In the nn-dlay cse, we will exhibit that a nonlinear differential equation of hematopoiesis model has a global attractor  for all different pstive solutions. Also, in the delay case, the sufficient conditions for the oscillation of all pstive solutions of it aboutare presented and we establish sufficient cnditions for the global attractive of. To illustrate the obtained results some examples are given.

Walter Lippmann, speaking about man, says : ” Gradually he makes for himself a trustworthy picture inside his head of the world beyond his reach. “. This means that the picture, whether it was good or bad, it doesn’t happen for nothing, but rather for intentional purposes. Some orientalists make their judgements even before getting to the place concerned with the study.

The mental image is one of the most misused terminology, although the world today has become the world of image, it witnessed the disappearance of the theories that used to consider the media as a reflective mirror for society, also it was confirmed that the media creates what varies from reality and sometimes completely different from reality. The image of

In this paper, a mathematical model consisting of the two harmful
phytoplankton interacting with a herbivorous zooplankton is proposed and studied.
The existence of all possible equilibrium points is carried out. The dynamical
behaviors of the model system around biologically feasible equilibrium points are
studied. Suitable Lyapunov functions are used to construct the basins of attractions
of those points. Conditions for which the proposed model persists are established.
The occurrence of local bifurcation and a Hopf bifurcation are investigated. Finally,
to confirm our obtained analytical results and specify the vital parameters, numerical
simulations are used for a hypothetical set of parameter values.

The ground pearls, Porphyrophora tritici (Bod.) is a new insect pest on wheat recorded for
the first time from Mousl Province, North of Iraq.

      Data security is an important component of data communication and transmission systems. Its main role is to keep sensitive information safe and integrated from the sender to the receiver. The proposed system aims to secure text messages through two security principles encryption and steganography. The system produced a novel method for encryption using graph theory properties; it formed a graph from a password to generate an encryption key as a weight matrix of that graph and invested the Least Significant Bit (LSB) method for hiding the encrypted message in a colored image within a green component. Practical experiments of (perceptibility, capacity, and robustness) were calculated using similarity measures like PSNR, MSE, and