In a connected graph , the distance function between each pair of two vertices from a set vertex  is the shortest distance between them and the vertex degree  denoted by  is the number of edges which are incident to the vertex  The Schultz and modified Schultz polynomials of  are have defined as:

 respectively, where the summations are taken over all unordered pairs of distinct vertices in  and  is the distance between  and  in  The general forms of Schultz and modified Schultz polynomials shall be found and indices of the edge – identification chain and ring – square graphs in the present work.

Let be an infinite dimensional separable complex Hilbert space and let , where is the Banach algebra of all bounded linear operators on . In this paper we prove the following results. If is a operator, then 1. is a hypercyclic operator if and only if D and for every hyperinvariant subspace of . 2. If is a pure, then is a countably hypercyclic operator if and only if and for every hyperinvariant subspace of . 3. has a bounded set with dense orbit if and only if for every hyperinvariant subspace of , .

Blogging is about more than just putting thoughts on a web; it's about connecting with and hearing from anyone who read the work. Many web sites now days help to get a free account to quick post thoughts and photos interact with people, and more. The fastest way to understand blogging is to try it out, but in that case securing the blog is important, by including authentication schemes. In this paper we suggest implications of our research for improving the design and usefulness of blogging systems, and also we divided the blogs depending on the subject and need, which are either to be used in public or only used by small group, so we can suggest different steps for securing the blogs.

Total of 170 samples were collected from Al-Chibayish Marsh reality in Dhi-Qar governorate southern of Iraq to study the epidemology of viral hepatitis in these areas and to detect the type of hepatitis viruses which include A ,B,C,D .The percentage of hepatitis A was 1.17% and most of them below age of ?10 (66.6%) while infection with hepatitis B account 5.29% and includes all age groups. There was no detected cases of hepatitis C,D. The laboratory study showed that the incidence of hepatitis B higher in male (4.11%) compared to female ( 2.35%)

    Shiranish has been studied at Hijran section near Erbil city, NE Iraq. Fifty two thin-sections were prepared to study them under polarized microscope, to determine the petrographic component, organic content and digenetic processes. Rock units subdivided into four rock beds, as follows: dolostone, foraminiferal biomicrite, poorly washed biomicrite and micrite. Vertical succession of Shiranish Formation refers to off-shore quite marine environment.

Countries have faced the challenges of high levels of public debt and seek to define the optimum limits to reduce risks to which the financial system can be exposed and its impact on the economy as a whole. Hence the importance of research in studying the impact of internal and external public debt components on indicators of stability of the financial system for the period 2005-2017 for the purpose of knowing the extent of the financial stability indicators response to the high level of the public debt from its optimum ratio, as the aim of the research is to estimate and analyze the dynamic relationship of short and long term between the components of public debt and indicators of financial stability using the (ARDL) model that