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.

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.

       ابو الفرج رونی از استادان شعر فارسی در دوره دوم غزنوی است.او در میان شاعران  ابو الفرج خیلی زودتر از دیگر شاعران  عصر خود متوجه نو کردن سبک سخن گردید چنان که میان روش او  وروش  معاصرانش از قبیل عثمان و مسعود سعد و معزی و نظایر آنان اختلافات فراوان وجود دارد. او طرز شعر دورهء اول غزنوی را که باید آن را سبک تکامل یافتهء دوره سامانی شمرد،  به دور افکند ، وطریقه ای جدید  پدید آورد. پژ

This paper has been taken out of a PhD dissertation titled "features of the political of Ali Al-Wardi" by the student Nahid Jaber Hassan .It was supervised by assistant professor Dr. Amer Hassan Faiyadh. Ali Al-Wardi (1913-1995) is a brilliant Iraqi Scientist. He wrote many scientific books. He created so many en lighted societal thoughts. Concerning the political affairs, Al-wardi presented opinions concerning the Iraqi Society based on the tri-concepts (The individual to be a good citizen, the society to be civic and the state to be modern). This paper is concerned with the uncovering of the concepts of authority and the state in the thinking's of Ali alwardi .He considered those variables as the basis of the tri-dimensional political

In this research, we attempt to show the extent of harmony in an aspect of the text according to the stylistics for the Knowing of the stylistic value of the title threshold, and the pathways of titles that suggest and support the meaning when the recipient reads the literary text, in addition to the interpretations that reflect the purposes of the poet who contributed to the drawing of his poetic achievement. The research presented a brief about the poet and his most important works, because they are the text which will be studied according to the stylistics. The research also explained the concept of style and the stylistics in the preface , because of the stylistic is the method adopted by the research to study the title thresholds in

   To investigate the research objectives, the researchers put the following hypothesis:

There was no statistically significant difference at the level of (0.05) between the average score of the students of the experimental group who studied the language of rhetoric according to model of learning method, and the average score of the students of the control group who studied the same article in the traditional way acquiring rhetorical concept.    The researchers relied on the experimental design with the partial setting of the post-test, which depends on the experimental group that is taught using the model of the learning method, and the control group taught using the traditional method.   

The operation of production planning is a difficult operation and it's required High effect and large time especially it is dynamic activity which it's basic variables change in continuous with the time, for this reason it needs using one of the operation research manner (Dynamic programming) which has a force in the decision making process in the planning and control on the production and its direct affect on the cost of production operation and control on the inventory.

The phenomenon of advertising In the poetry of Ali bin Abdul Rahman Balnopi Sicilian