Throughout this paper we study the properties of the composition operator
C
p1  o
p2  o…o
pn  induced by the composition of finite numbers of special
automorphisms of U,
pi  (z)  i
i
p z
1 p z


Such that pi  U, i  1, 2, …, n, and discuss the relation between the product of
finite numbers of automorphic composition operators on Hardy space H2 and some
classes of operators.

The concept of forming the living space in the American strategic thought has an
important position it is regarded as an strategic movement that it supports the American
United States with the huge capabilities in its own concern that enables it to approach of
American administration , we find that of different historical periods it works to establish that
the geopolitical dimension which is accompanied with the ability of American response for
the evens that in its own turn enables the American united states to seize the growing chances
in the global strategic environment This study includes five chapters :
- Chapter one: The idea of living space.
- Chapter two: Geopolitical dimension of living space theory.
-

     By definition, the detection of protein complexes that form protein-protein interaction networks (PPINs) is an NP-hard problem. Evolutionary algorithms (EAs), as global search methods, are proven in the literature to be more successful than greedy methods in detecting protein complexes. However, the design of most of these EA-based approaches relies on the topological information of the proteins in the PPIN. Biological information, as a key resource for molecular profiles, on the other hand, acquired a little interest in the design of the components in these EA-based methods. The main aim of this paper is to redesign two operators in the EA based on the functional domain rather than the graph topological domain. The perturb

A simple straightforward mathematical method has been developed to cluster grid nodes on a boundary segment of an arbitrary geometry that can be fitted by a relevant polynomial. The method of solution is accomplished in two steps. At the first step, the length of the boundary segment is evaluated by using the mean value theorem, then grids are clustered as desired, using relevant linear clustering functions. At the second step, as the coordinates cell nodes have been computed and the incremental distance between each two nodes has been evaluated, the original coordinate of each node is then computed utilizing the same fitted polynomial with the mean value theorem but reversibly.

The method is utilized to predict

The present work determines the particle size based only on the number of tracks detected in a cluster created by a hot particle on the CR-39 solid state nuclear track detector and depending on the exposure time. The mathematical model of the cross section developed here gives the relationship between alpha particle emitting from the (n, α) reaction and the number of tracks created and distribution of tracks created on the surface of the track detector. In an experiment performed during this work, disc of boron compound (boric acid or sodium tetraborate) of different weights were prepared and exposed to thermal neutron from the source. Chemical etching is processes of path formation in the detector, during which a suitable etching solut

Background: The prediction of changes in the mandibular third molar position and eruption is an important clinical concern because third molar retention may be beneficial for orthodontic anchorage. The aims of this study were to assess the mandibular third molar position by using medical CT scan and lateral reconstructed radiograph and evaluate gender differences. Materials and Methods: The sample of present study consisted of 39 patients (18 males and 21 females) with age range 11-15 years who were attending at Al-Suwayra General Hospital/ the Computerized Tomography department. The distance from anterior edge of ramus to distal surface of permanent mandibular second molar and mesio-distal width of developing mandibular third molar were

Space is considered as an important element in constructing artwork, it can be a dominant and fulfilled part that adds new existence to the content. Each artwork must have a space artistically or analytically. The internal and eternal space of artwork have associated with each other in order to be ann important connected unit that establishes the work epressions and helps the audience to understand it. Such kind of works can be represented by the works of the potter (Sheinyor Abdu Allah) which have uarious expressions of space which this study is based on.The study aims at finding out the treatment of apace in the ceramic sculpture works of the potter (Sheinyar Abdu Allah).The second chapter has many sections. T