Given a discrete semi-group $S$, we define a topological ACTION $\theta$ of S on a locally compact space $X$. Additionally, there is an ACTION α of $S$ on the $C^∗$-algebra $C0(X)$, which is introduced in relation to $θ$. We explore the topological independence of $\theta$ and the impact of $\theta$ on α. Finally, we discuss the concept of a semi-PARTIAL dynamical system $(C0(X), S, \alpha)$ and examine some of its properties.

Some PARTIAL ACTION properties of a group G on a C*-algebra A are extended to an ACTION of a unital inverse semigroup S on C0(X). Also, invariant and quotient ideals of C0(X)×aS are considered.

Introduction: Effective plaque removal is an important factor in the long-term clinical success of dental implants. The aim of this study was to compare the clinical efficacy of a powered toothbrush (Power Cross-ACTION) and a manual toothbrush (Cross-ACTION) in the control of plaque and soft tissue inflammation around implants supporting mandibular overdentures.Materials and Methods: This study was a cross-over clinical trial. The subjects included 10 edentulous subjects, aged 47-73 years, with removable mandibular overdentures supported by 2 unsplinted implants, all the subjects wore maxillary complete dentures. The study consisted of two 4-week phases separated by a 2-week interval. In each phase each subject randomly used one toothbrush type. Two days prior to each phase, the implants were polished. Plaque and bleeding indices were recorded before and after brushing. Data was analyzed by t-test using SPSS software (a=0.05).Results: Both toothbrushes reduced the indices under study. Means of plaque index decreases were 0.5 in manual toothbrush and 0.44 in powered toothbrush. Means of bleeding index decreases were 0.27 in manual toothbrush and 0.3 in powered toothbrush. There were no statistically significant differences between the two toothbrush types in changing plaque index (p value=0.88) and bleeding index (p value=0.91).Conclusion: Both toothbrushes were efficient in plaque control around implants which supported mandibular overdentures and there was no difference between them. Patients can use one of these toothbrushes depending on personal preference and comfort.

Objective: Mechanical plaque removal namely tooth brushing is the most commonly used oral hygiene technique. Efficacy of tooth brushing is influenced by the design and shape of toothbrush. This study aimed to compare the efficacy of two common Iranian toothbrushes with a foreign made one in plaque removal.Methods: This clinical trial was conducted on 30 female dental students in Babol University, School of Dentistry using simple randomized sampling. Oral B Cross ACTION(Germany), Panberes Cross ACTION and Panberes Classic (Iran) toothbrushes were compared. Students were asked not to brush their teeth for 24 hours before the first visit. At the first visit, subjects received oral prophylactic procedures and the baseline plaque index was recorded before brushing for all subjects using 0' Leary plaque index. In order to match the conditions, Bass tooth brushing technique was instructed to subjects. Students were then randomly divided into 3 groups of 10. The subjects were provided with the three toothbrushes for use in the first, second and third weeks. The plaque index was recorded after using each toothbrush for one week. Paired t-test was used to compare the efficacy of toothbrushes in plaque removal in the same subject while ANOV A was applied for the comparison between the three toothbrushes.Results: Significant reductions were observed in plaque index after using each toothbrush. Plaque index reduction was the highest for Oral B Cross ACTION and the lowest for Panberes Classic (P=0.001). Oral B Cross ACTION and a significant difference with Panberes Classic in mean plaque index reduction (P=0.018). Panberes Cross ACTION and Oral B Cross ACTION were not significantly different in this respect (P=0=797).Conclusion: Oral B Cross ACTION and Panberes Cross ACTION were not significantly different in terms of plaque index reduction. However, the mentioned two toothbrushes had a significant difference in this respect with Panberes Classic.

Introduction: Arbitration has a contractual nature and is subject to the sovereignty of the will of the parties, but in some cases, the legislator imposed the referral of claims to arbitration on the will of the parties and caused the contractual nature of the arbitration clause to disappear or be limited. By doing this, he has placed the arbitration outside the will of the parties. This issue causes some moral conflicts in the discussion of compulsory arbitration. Therefore, this research has been done with the purpose of examining the position of compulsory arbitration in Iran's legal system and the ethical challenges in it with a descriptive-analytical approach. Material and Methods: The research was a review method, in order to achieve the goal of the research, in addition to electronic education books and virtual education in this field, articles related to the research keywords from 2004 to 2022 from the databases of Civilica, Magiran, Sid, Researchgate, Science direct, was reviewed Conclusion: Based on the findings of the research, it can be concluded that compulsory arbitration in Iran has ethical challenges in the field of implementation and interpretation, the most important of which is the issue of the right to ACTION and judicial justice. In the context of ambiguities in mandatory arbitration, even if the method of arbitration becomes ambiguous, the arbitrator has the duty to find out the will of the legislator with the principles and rules of interpretation, which creates a moral conflict for the arbitrator.