we applied the direct product concept on the notation of intuitionistic fuzzy semi d-ideals of d-algebra with investigation some theorems, and also, we study the notation of direct product of intuitionistic fuzzy topological d-algebra.

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.

In the present paper, the concepts of a quasi-metric space, quasi-Banach space
have been introduced. We prove some facts which are defined on these spaces and
define some polynomials on quasi-Banach spaces and studied their dynamics, such
as, quasi cyclic and quasi hypercyclic. We show the existence of quasi chaotic in the
sense of Devaney (quasi D-chaotic) polynomials on quasi Banach space of qsummable
sequences lq , 0<q<1 such polynomials P is defined by P((xi)i)=(p(xi+m))i
where p:CC, p(0) = 0. In general we also prove that P is quasi chaotic in the sense
of Auslander and Yorke (quasi AY-chaotic) if and only if 0 belong to the Julia set of
p, mN. And then we prove that if the above polynomial P o

     This article is devoted to presenting results on invariant approximations over a non-star-shsped weakly compact subset of a complete modular space by introduced a new notion called S-star-shaped with center f:  if   be a mapping and , . Then the existence of common invariant best approximation is proved for Banach operator pair of mappings by combined the hypotheses with Opial’s condition or demi-closeness condition

In this paper the research introduces a new definition of a fuzzy normed space then the related concepts such as fuzzy continuous, convergence of sequence of fuzzy points and Cauchy sequence of fuzzy points are discussed in details.

Supra nanoparticles (submicron) of Chicken bones fibers were used (before and after treated with citric acid solution) as additives  to dental composite with the weight ratios (1%, 2% and 4%). The main mechanical tests represented by hardness, wear resistance and compression strength was carried out on the improvement dental composites.

The addition of treated supra nanoparticles Chicken thigh bones with particles size (300 nm) by weight ratio (1%) to ordinary dental composite resin , significantly improves all of its mechanical properties, in addition to the increase the value of the its  glass transition temperature from  43^oC  to 45.4 ^oC. The techniques X-ray diffraction (XRD), Energy Dispersive Spectr

In this paper the definition of fuzzy normed space is recalled and its basic properties. Then the definition of fuzzy compact operator from fuzzy normed space into another fuzzy normed space is introduced after that the proof of an operator is fuzzy compact if and only if the image of any fuzzy bounded sequence contains a convergent subsequence is given. At this point the basic properties of the vector space FC(V,U)of all fuzzy compact linear operators are investigated such as when U is complete and the sequence ( ) of fuzzy compact operators converges to an operator T then T must be fuzzy compact. Furthermore we see that when T is a fuzzy compact operator and S is a fuzzy bounded operator then the composition TS and ST are fuzzy compact

Despite ample research on soft linear spaces, there are many other concepts that can be studied. We introduced in this paper several new concepts related to the soft operators, such as the invertible operator.  We investigated some properties of this kind of operators and defined the spectrum of soft linear operator along with a number of concepts related with this definition; the concepts of eigenvalue, eigenvector, eigenspace are defined. Finally the spectrum of the soft linear operator was divided into three disjoint parts.

     According to the high operational costs, low stability, and reusability of enzymes, immobilization by nanoparticle gathering has increased in recent years. Iron oxide nanoparticles (magnetite nanoparticles, Fe₃O₄) have been prepared by mixing one volume of iron dioxide ions and two volumes of iron trioxide ions with HCl via the precipitation of iron salts by NH₄OH. The features of magnetic nanoparticles have been studied by Atomic Force Microscopy (AFM), X-Ray Diffraction (XRD), Fourier Transform Infrared Spectroscopy, and Scanning Electron Microscopy (SEM). The prepared Fe₃O₄ was used in the adsorption method to immobilize the galactosidase enzyme. The immobilized enzyme has been compared wi