The objective of this paper is, firstly, we study a new concept noted by algebra and discuss the properties of this concept. Secondly, we introduce a new concept related to the algebra such as smallest algebra. Thirdly, we introduce the notion of the restriction of algebra on a nonempty subset  of and investigate some of its basic properties. Furthermore, we present the relationships between field, monotone class, field and algebra. Finally, we introduce the concept of measure relative to the algebra and prove that every measure relative to the   is complete.

In this paper, the definition of fuzzy anti-inner product in a linear space is introduced. Some results of fuzzy anti-inner product spaces are given, such as the relation between fuzzy inner product space and fuzzy anti-inner product. The notion of minimizing vector is introduced in fuzzy anti-inner product settings.

 We use the idea of Grill, this study generalized a new sort of linked space like –connected –hyperconnected and investigated its features, as well as the relationship between it and previously described notation. It also developed new sorts of functions, such as hyperconnected space, and identifying their relationship, by offering numerous instance and attributes that belong to this set. This set will serve as a starting point for further research into the sets many future possibilities. Also, we use some of the theorems and observations previously studied and relate them to the grill and the Alpha group, and benefit from them in order to obtain new results in this research. We applied the concept of Connected to them and obtained

In this paper, we analyze several aspects of a hyperbolic univalent function related to convexity properties, by assuming  to be the univalent holomorphic function maps of the unit disk  onto the hyperbolic convex region  ( is an open connected subset of). This assumption leads to the coverage of some of the findings that are started by seeking a convex univalent function distortion property to provide an approximation of the inequality and confirm the form of the lower bound for . A further result was reached by combining the distortion and growth properties for increasing inequality  . From the last result, we wanted to demonstrate the effect of the unit disk image on the condition of convexity estimation

 Let  be a metric space and  be a continuous map. The notion of the  -average shadowing property ( ASP )  for a continuous map on  â€“space is introduced  and the relation between the ASP and average shadowing property(ASP)is investigated. We show that if  has ASP, then   has ASP for every . We prove that if a map  be pseudo-equivariant with dense set of periodic points and has the ASP,  then  is weakly mixing. We also show that if   is a expansive pseudo-equivariant homeomorphism that has the ASP and  is topologically mixing,  then  has a  -specification. We obtained that the identity map  on  has the ASP  if and only if th

 The study aimed to prepare psychological measures of intellectual emptiness and mental distraction on university students. The two researchers used the descriptive approach in the two methods of surveying and correlational relations to suit the nature of the research, where the study sample consisted of (101) students of physical education and sports sciences.  The phrase- Intellectual emptiness(35) and (34) is a phrase for mental distraction and presented it to experts in psychology, testing and measurement, and the statistical bag for social sciences (spss) was used, and the results of the research showed that intellectual emptiness has a moral relationship with straying among some students of the College of Physical Education

The importance of the study, which is how to use these exercises with the device in rehabilitating the flabby muscles after childbirth, which is a problem found in our society and in need of high education on it because the form of exercises does not need places designated for training such as halls or fitness halls, especially since the social woman has limited movement in which we see the responses Physiology in different ways, the woman’s body is not only subject to the day’s need for work or the need to complete hours of physical training, but she has feminist components that she must overcome, whether it is physiological or otherwise.The research sample was determined by the intentional method available from women whose age