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,

Diazotization reaction between quinolin-2-ol and (2-chloro-1-(4-(N-(5-methylisoxazol-3-yl)sulfamoyl)phenyl)-2l4-diazyn-1-ium was carried out resulting in ligand-HL, this in turn reacted with the next metal ions (Ni²⁺, Pt⁴⁺, Pd²⁺, and Mn²⁺)  forming stable complexes with unique geometries such as (tetrahedral for both Ni²⁺ and Mn²⁺, octahedral for Pt⁴⁺ and square planer for Pd²⁺ ). The creation of such complexes was detected by employing spectroscopic means involving ultraviolet-visible which proved the obtained geometries, fourier transfer proved the formation of azo group and the coordination with metal ion through it. Pyrolysis (TGA &

In this work, the precursor [2-(1,5-dimethyl-3-oxo-2-phenyl-2,3-dihydro-1H-pyrazol-4-ylimino)acetic acid] was synthesised from 4-aminoantipyrine and glyoxylic acid, this precursor has been used in the synthesis of new multidentate ligand [2-((E)-3-(2-hydroxyphenylimino)-1,5-dimethyl-2-phenyl-2,3-dihydro-1H-pyrazol-4-ylimino)acetic acid][H2L] type (N2O2). The ligand was refluxed in ethanol with metal ions [VO(II), Mn(II), Co(II) and Ni(II)] salts to give complexes of general molecular formula:[M(H2L)2(X)(Y)].B, where: M=VO(II), X=0, Y=OSO3-2, B=2H2O; M=Mn(II),Co(II) ,X=Cl, Y=Cl, B=0; M=Ni(II), X=H2O, Y=Cl, B=Cl. These complexes were characterised by atomic absorpition(A.A), F.T-I.R., (U.V-Vis)spectroscopies (1H,13C NMR for ligand only), alon

The change in the optical band gap and optical activation energy have been investigated for pure Poly (vinyl alcohol)and Poly (vinyl alcohol) doped with Aluminum sulphate to proper films from their optical absorption spectra. The absorption spectra were measured in the wave range from (200-700) nm at temperature range (25-140) 0C. The optical band gap (Eg) for allowed direct transition decrease with increase the concentration of Aluminum sulphate. The optical activation energy for allowed direct transition band gap was evaluated using Urbach- edges method. It was found that ?E increases with increasing the concentration of Al2 (SO4)3 and decreases when temperature increases.

A new Schiff base of HL has been synthesized from amoxicillin drug and 4- Chlorobenzophenone. Cr (III), Fe (III), Co (II), Ni (II), Cu (II), Cd (II) and Hg (II) mixed ligands complexes of Schiff base and Nicotinamide. Diagnosis of synthesis ligand and its complexes are done by 1HNMR, 13CNMR and thermal analysis for HL ligand, FTIR, UV-visible, molar conductance, CHN analysis, magnetic susceptility and atomic absorption. Octahedral geometries have been suggested for all complexes. All compounds under study were tested antimicrobial activity against four type of bacteria such as Pseudomonas aeruginosa, Escherichia coli, Staphylococcus aureus Bacillis subtilis in nutrient agar.

D-mannose sugar was used to prepare [benzoic acid 6-formyl-2, 2-dimethyl-tetrahydrofuro [3, 4-d][1, 3] dioxol-4-yl ester](compound A). The condensation reaction of folic acid with (compound A) resulted in the formation of new ligand [L]. These compounds were characterized by elemental analysis CHN, atomic absorption AA,(FT-IR),(UV-Vis), TLC, ES mass (for electrospray), molar conductance, and melting point. The new tetradentate ligand [L], reacted with two moles of some selected metal ions and two moles of (2-aminophenol),(metal: ligand: 2-aminophenol) at reflux in water medium to give a series of new complexes of the general formula K2 [M2 (L)(HA) 2] where M= Co (II), Ni (II), Cu (II) and Cd (II). These complexes were characterized by eleme

Previous studies on the synthesis and characterization of metal chelates with uracil by elemental analysis, conductivity, IR, UV-Vis, NMR spectroscopy, and thermal analysis were covered in this review article. Reviewing these studies, we found that uracil can be coordinated through the electron pair on the N1, N3, O2, or O4 atoms. If the uracil was a mono-dentate ligand, it will be coordinated by one of the following atoms: N1, N3 or O2. But if the uracil was bi-dentate ligand, it will be coordinated by atoms N1 and O2, N3 and O2 or N3 and O4. However, when uracil forms complexes in the form of polymers, coordination occurs through the following atoms: N1 and N3 or N1 and O4.