In this paper, we define some generalizations of topological group namely -topological group, -topological group and -topological group with illustrative examples. Also, we define grill topological group with respect to a grill. Later, we deliberate the quotient on generalizations of topological group in particular -topological group. Moreover, we model a robotic system which relays on the quotient of -topological group.

The objective of this paper is to study the dependent elements of a left (right)
reverse bimultipliers on a semiprime ring. A description of dependent elements of
these maps is given. Further, we introduce the concept of double reverse ( , )-
Bimultiplier and look for the relationship between their dependent elements.

     In this paper we tend to describe the notions of intuitionistic fuzzy asly ideal of ring indicated by (I. F.ASLY) ideal and, we will explore some properties and connections about this concept.

     Suppose that F is a reciprocal ring which has a unity and suppose that H is an F-module. We topologize La-Prim(H), the set of all primary La-submodules of H , similar to that for FPrim(F), the spectrum of fuzzy primary ideals of F, and examine the characteristics of this topological space. Particularly, we will research the relation between La-Prim(H) and La-Prim(F/ Ann(H)) and get some results.

Single crystals of pure and Cu+2,Fe+2 doped potassium sulfate were grown from aqueous solutions by the slow evaporation technique at room temperature. with dimension of (11x9 x4)mm3 and ( 10x 8x 5)mm3 for crystal doping with Cu &Fe respectively. The influence of doping on crystal growth and its structure revealed a change in their lattice parameters(a=7.479 Ã… ,b=10.079 Ã… ,c=5.772 Ã…)for pure and doping (a=9.687 Ã…, b=14.926 Ã… ,c= 9.125 Ã…) & (a=9.638 Ã… , b= 8.045 Ã… ,c=3.271 Ã…) for Cu & Fe respectively. Structure analysis of the grown crystals were obtained by X-Ray powder diffraction measurements. The diffraction patterns were analyzed by the Rietveld refinement method. Rietveld refinement plo

            In this paper, the Normality set  will be investigated. Then, the study highlights some concepts properties and important results. In addition, it will prove that every operator with normality set has non trivial invariant subspace of  .

An algebra has been constructed from a (D, A)-stacked algebra A, under the conditions that , A 1 and . It is shown that when the construction of algebra B is built from a (D, A)-stacked monomial algebra A then B is a d-Koszul monomial algebra.

This paper deal with the estimation of the shape parameter (a) of Generalized Exponential (GE) distribution when the scale parameter (l) is known via preliminary test single stage shrinkage estimator (SSSE) when a prior knowledge (a₀) a vailable about the shape parameter as initial value due past experiences as well as suitable region (R) for testing this prior knowledge.

The Expression for the Bias, Mean squared error [MSE] and Relative Efficiency [R.Eff(×)] for the proposed estimator are derived. Numerical results about beha

Let M be a n-dimensional manifold. A C1- map f : M  M is called transversal if for all m N the graph of fm intersect transversally the diagonal of MM at each point (x,x) such that x is fixed point of fm. We study the minimal set of periods of f(M per (f)), where M has the same homology of the complex projective space and the real projective space. For maps of degree one we study the more general case of (M per (f)) for the class of continuous self-maps, where M has the same homology of the n-dimensional sphere.