Continuous functions are novel concepts in topology. Many topologists contributed to the theory of continuous functions in topology. The present authors continued the study on continuous functions by utilizing the concept of gpα-closed sets in topology and introduced the concepts of weakly, subweakly and almost continuous functions. Further, the properties of these functions are established.

Let
be a dynamical system,
is said to be topological transitive if for every pair of non-empty open set
, there exists
such that
. We introduce and investigate a new definition of topological transitive by using the nation N-open subset and we called N-transitive and prove the equivalent definitions of this new definition.

The aim of this paper is to prove some results for equivalence of moduli of smoothnes in approximation theory , we used a"non uniform" modulus of smoothness and the weighted Ditzian –Totik moduli of smoothness in by spline functions ,several results are obtained .For example , it shown that ,for any the inequality , is satisfied ,finally, similar result for chebyshev partition and weighted Ditzian –Totik moduli of smoothness are also obtained.

During the ongoing economic revolutions of the economic There is a new economic revolution is emboded by upseting the balances of prevailing classic ideas and refusing axioms considered postulates which were not touched including, for example, the theory of ( supply and demand) espoused by (Adam Smith and Marshall and others ) that assumes the existence of a strong relationship between the supply of goods and services and the demand for them, in the light of successive economic developments, considerable technological progress and the information revolution of the complex telecommunication network led to a serious shift of this theory and the emergence of a new theory called (market economies) turned the traditional scales of production,

The charge transfer at C23H17F8N8O2PRu, C44H30BF4N5O4Ru, C56H52CL5N5OOsP2 and C76H88F80N24O11P10Ru4 nitrosyl complexes are investigation and studies theoretically using the quantum consideration. Charge transfer behavior largely rely to the electric properties of nitrosyl complexes system whose depending on the main important parameters for the transmission rate constant such that: orientation transition energy, overlapping coupling coefficient, driving force energy, height barrier and Temperature T (K). Data results have been evaluated using a MATLAB program. Results show that rate of charge transfer increases due to increases the orientation transition energy.

Based on the density functional theory (DFT) , the stability of molecular complexes has been predicted according to hard-soft acid base (HSAB) theory. Relative stability of products and reactivity of soft base sulfide derivatives with halogens (Iodine , Bromine , Chlorine) as soft acid was studied to determine the relative ability of these reactants causing the reaction to be more spontaneous.
DFT at the levels of B3LYP/3-21G and B3LYP/3-21G (d) was used to study HOMO LUMO energy gaps , bonds length and total energy to calculate the softness sequence of each type of acid or base mentioned in this work. All cases studied prove that iodine can be considered as the most softness acid and ethyl methyl sulfide≈ dimethyl sulfide the most

Cerium (III), Neodymium (III) and Samarium (III) Complexes existent a wide range of implementation that stretch from their play in the medicinal and pharmaceutical area because of their major significant pharmacological characteristic such as antifungal, anti-cancer, anti-bacterial ,anti-human immunodeficiency virus ,antineoplastic, anti-inflammation,inhibition corrosion,in some industrial (polymers, Azo dye).It is likely to open avenuesto research among various disciplines such as physics, electronics, chemistry and materials science by these complexes that contain exquisitely designed organic molecules.This paper reviews the definition, importance and various applications of Cerium (III), Neodymium (III) and Samarium (III) Complexe

The aim of this study is to synthesize an easy, non-toxic and eco-friendly method. Silver nanoparticles which were synthesized by leaf extract of mint were characterized by UV-Visible Spectroscopy which appears UVVisible spectrum of demonstrated a peak 448 nm corresponding to surface Plasmon resonance of silver nanoparticles, Fourier Transform Infrared Spectroscopy (FTIR); functional groups involved in the silver nanoparticles synthesis were identified, the presence of silver nanoparticles was confirmed by X-ray diffraction (XRD) and Atomic Force Microscope (AFM) analysis clearly illustrated that the shape of silver nanoparticles was spherical and the size of the silver nanoparticles has been measured as 55- 85 nm. Evaluation of its antimic