Relation on a set is a simple mathematical model to which many real-life data can be connected. A binary relation  on a set  can always be represented by a digraph. Topology on a set  can be generated by binary relations on the set . In this direction, the study will consider different classical categories of topological spaces whose topology is defined by the binary relations adjacency and reachability on the vertex set of a directed graph. This paper analyses some properties of these topologies and studies the properties of closure and interior of the vertex set of subgraphs of a digraph. Further, some applications of topology generated by digraphs in the study of biological systems are cited.

Background: Kinesiologists, Physical Anthropologists, and Anatomists have all long been captivated by the structure and development of the superficial forearm flexor, the Palmaris longus.

Objective: To study the effect of Palmaris Longus on certain handwriting skills.

Subjects and Methods: Three Palmaris Longus occurrence tests were conducted on 200 students (100 males and 100 females) affiliated to Colleges of Medicine of Baghdad University then the participants were tested for certain handwriting skills to correlate the presence of Palmaris Longus in the dominant side with handwriting.

Results: 89% of all subject

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.

     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

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.

The purpose of this paper is to study the instability of the zero solution of some type of nonlinear delay differential equations of fourth order by using the Lyapunov-Krasovskii functional approach; we obtain some conditions of instability of solution of such equation.

The purpose of this paper is to study the instability of the zero solution of some type of nonlinear delay differential equations of fifth order with delay by using the Lyapunov-Krasovskii functional approach, we obtain some conditions of instability of solution of such equation.