The purpose of this paper is to study a new types of compactness in the dual bitopological spaces. We shall introduce the concepts of L-pre- compactness and L-semi-P- compactness .

The theory of general topology view for continuous mappings is general version and is applied for topological graph theory. Separation axioms can be regard as tools for distinguishing objects in information systems. Rough theory is one of map the topology to uncertainty. The aim of this work is to presented graph, continuity, separation properties and rough set to put a new approaches for uncertainty. For the introduce of various levels of approximations, we introduce several levels of continuity and separation axioms on graphs in Gm-closure approximation spaces.

The purpose of this paper is to find the best multiplier approximation of unbounded functions in    –space by using some discrete linear positive operators. Also we will estimate the degree of the best multiplier approximation in term of modulus of continuity and the averaged modulus.

The  purpose  of  the  paper  is  to  tind  the  degree  of  the approximation of a functions  f be bounded , measurable and defined

in  interval   [a,h]by  Bernstein  polynomial  in  LP    space  1 $ p < oo by

using Ditzian-Totik modulus  of smootlmess  and  k 1n  average modvlus of smoothness.

The purpose of this paper is to introduce and prove some coupled coincidence fixed point theorems for self mappings satisfying -contractive condition with rational expressions on complete partially ordered metric spaces involving altering distance functions with mixed monotone property of the mapping. Our results improve and unify a multitude of coupled fixed point theorems and generalize some recent results in partially ordered metric space. An example is given to show the validity of our main result. 

The electric quadrupole moments for some nitrogen isotopes (12,14,15,16,18N) are
studied by shell model calculations with the proton-neutron formalism. Theoretical
calculations performed using the different set of effective charges due to the core
polarization effect. The effective charges in the p-shell nuclei are found to be
slightly different from those in the sd-shell nuclei. Most of the results we have
obtained are underestimated with the measured data for the isotopes considered in
this work.

     In this paper, we introduce new definitions of the - spaces  namely the    - spaces  Here,  and  are natural numbers that are not necessarily equal, such that . The space  refers to the n-dimensional Euclidean space,  refers to the quaternions set and  refers to the N-dimensional quaternionic space. Furthermore, we establish and prove some properties of their elements. These elements are quaternion-valued N-vector functions defined on , and the  spaces  have never been introduced in this way before.

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.

   In this paper we obtain some statistical approximation results for a general class of maxproduct operators including the paused linear positive operators.

In this paper, we introduced some new definitions on P-compact topological ring and PL-compact topological ring for the compactification in topological space and rings, we obtain some results related to P-compact and P-L compact topological ring.