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.

Cryptographic applications demand much more of a pseudo-random-sequence
generator than do most other applications. Cryptographic randomness does not mean just
statistical randomness, although that is part of it. For a sequence to be cryptographically
secure pseudo-random, it must be unpredictable.
The random sequences should satisfy the basic randomness postulates; one of them is
the run postulate (sequences of the same bit). These sequences should have about the same
number of ones and zeros, about half the runs should be of length one, one quarter of length
two, one eighth of length three, and so on.The distribution of run lengths for zeros and ones
should be the same. These properties can be measured determinis

The study aimed to build a suggested conception for employing gamification in teaching the general education curricula. Using the analytical method of the previous analytical studies in Teaching, which agreed with the determinants of the analysis of 20 studies from 2014 to 2019, they come on order: points, badges, leaderboards, and then levels. The four most commonly used theories are the theory of self-determination, flow theory, the theory of planned behavior and social theory. In addition, the researcher identified the most commonly used models in gamification, respectively: the ARCS model and the user-based design model. Based on the results of the analysis and using the descriptive approach, the researcher presented a practical perc

In this research, the Williamson-Hall method and of size-strain plot method was employed to analyze X- ray lines for evaluating the crystallite size and lattice strain and of cadmium oxide nanoparticles. the crystallite size value is (15.2 nm) and (93.1 nm) and lattice strain (4.2 x10−4 ) and (21x10−4) respectively. Also, other methods have been employed to evaluate the crystallite size. The current methods are (Sherrer and modified Sherrer methods ) and their results are (14.8 nm) and (13.9nm) respectively. Each method of analysis has a different result because the alteration in the crystallite size and lattice strain calculated according to the Williamson-Hall and size-strain plot methods shows that the non-uniform strain in nan

This research deals with the motives of the use of Facebook by elderly people and the achieved needs, which leads the researcher to ask an important question: why an old persons use Facebook and are the achieved needs through   which they got?  The research aims to find out the habits and patterns of using Facebook by old men and stands on the main motives of the elderly in their use of Facebook. It also identifies the most prominent needs that have been made for the elderly as a result of their use of Facebook.

The research is a descriptive one in which the researcher uses survey method to achieve the desired goals. The researcher has chosen a group of old men from Diyala province. The total sample number is about

The research aims to study some of the human characteristics of the state of Singapore to know the impact of these characteristics on the strength of the state, its development and. The research included two aspects, theoretical and analytical, using the descriptive analytical method, force analysis method, as well as the historical method. The data was analyzed according to mathematical equations, including the size of the country's population, the extraction of the population growth rate and the concept of age structure, where some indicators related to this concept have been explained. The researcher reached a set of results, the most important of which were: that the population size of the state of Singapore in the period between (19

Abstract
On 11/1/2008 amounts of snows fell on various sections of Iraq, one of
which is Baghdad. The analysis process of climatic maps proved that the
advance trough of Sudanese depression towards the city is the reason behind
the formation of this weather state supported by could trough in the (500) mb
pressure level. .
The research concluded that the phenomenon of global warming
witnessed by the world recently had a main role in the occurrence of this
phenomenon due to the raise in earth temperature as a result of evaporation
rate increase leading to an increase in water vapor and cloud formation with
high tops and low bases which form sows with high rates accumulating at high
and moderate latitudes le

Background: footballers may have poor oral health like elevated levels of dental caries. The purpose of this study was to estimate the prevalence and severity of dental caries in Iraqi footballers and to measure dental treatments needs. Materials and methods: 403 Iraqi males footballers aged from 18-32 years were included in the study. The cases were recruited from 18 clubs in Baghdad city. Results: the results of present study showed increased percent of caries experience according to age increase and decreased dental caries percent as education level increased among Iraqi footballers. Decayed component was found to be the largest of DMFS value compared to MS and FS among all age groups, Caries experience was found to be increased as age

Back ground: Dental caries and periodontal disease followed by enamel defect were the most common and widely spread diseases affecting children. Aim of this study is the assessment of the occurrence and severity of dental caries, dental plaque, gingivitis and enamel anomalies among 4-5 years old children in Karbala city-Iraq. Materials and methods: A sample of 658 children (350 males, 308 females) aged four and five years old was selected randomly from the fourteenth kindergartens in Karbala city. Diagnosis and recording of dental caries and enamel anomalies were followed the criteria of WHO 1987, WHO1997 respectively. Dental plaque was assessed using plaque index of Silness and Loe,1964. Gingival health condition was assessed using gingiv