The aim of our work is to develop a new type of games which are related to (D, WD, LD) compactness of topological groups. We used an infinite game that corresponds to our work. Also, we used an alternating game in which the response of the second player depends on the choice of the first one. Many results of winning and losing strategies have been studied, consistent with the nature of the topological groups. As well as, we presented some topological groups, which fail to have winning strategies and we give some illustrated examples. Finally, the effect of functions on the aforementioned compactness strategies was studied.  

Background: The base of the denture is largely responsible for providing the prosthesis with retention, stability, and support by being closely adapted to the oral mucosa. However; the process of bone resorption is irreversible and may lead to an inadequate fit of the prosthesis; this can be overcome by relining. Materials and methods: Acrylic based soft denture liner is prepared by preparing polymer from purified methylmethacrylate monomer with (10-2) initiator and (30%) dibutylphthalate plasticizer concentrations. Biological properties were evaluated in comparison with the control material through subcutaneous specimens' implantation in the New Zealand rabbits. Excisional biopsies were taken after (1, 3, days 1, 2, 3, 4 weeks) period. Mic

Background: The study aimed to investigate the effect of different techniques of en masse retraction on the vertical and sagittal position, axial inclination, rate of space closure, and type of movement of maxillary central incisor. Materials and methods: A typodont simulation system was used (CL II division 2 malocclusion). Three groups were used group 1(N=10, T-loop), group 2(N=10, Time-Saving loop), and group 3(N=10, Microimplant). Photographs were taken before and after retraction and measurements were made using Autodesk AutoCAD© software 2010. Kruskal-Wallis one-way analyses of variance and Mann-Whitney U test (p?0.05) were used. Results: The rate of space closure showed no significant difference among the three groups (p?0.05), whi

In this paper the definition of fuzzy normed space is recalled and its basic properties. Then the definition of fuzzy compact operator from fuzzy normed space into another fuzzy normed space is introduced after that the proof of an operator is fuzzy compact if and only if the image of any fuzzy bounded sequence contains a convergent subsequence is given. At this point the basic properties of the vector space FC(V,U)of all fuzzy compact linear operators are investigated such as when U is complete and the sequence ( ) of fuzzy compact operators converges to an operator T then T must be fuzzy compact. Furthermore we see that when T is a fuzzy compact operator and S is a fuzzy bounded operator then the composition TS and ST are fuzzy compact

Background: Complete removal of filling material from the root canal is an essential requirement for endodontic retreatment. The purpose of the present study is to evaluate and compare the dissolving capabilities of various solvents (Xylene, Eugenate Desobturator, Eucalyptol, EDTA and Distilled water (as a control)) on four different types of sealer (Endofill, Apexit Plus, AH Plus and EndoSequence bioceramic sealer). Materials and method: Eighty samples of each sealer were prepared according to the manufacturers' instructions and then divided into ten groups (of 8 samples) for immersion in the respective solvents for 2 and 5 min immersion periods. Each sealer specimen was weighed to obtain its initial mass. The specimens were immersed in

Background: The elimination of the microorganisms from the root canal systems, an important step for the successful root canal treatment. This study was conducted to evaluate the antibacterial effectiveness of the photoactivated disinfection by using the toluidine blue O and a low- energy light emitting diode (LED) lamp . Materials and method: Sixty single rooted extracted teeth were decoronated, instrumented, irrigated, sealed at the apex and contaminated with endodontic anaerobic bacteria for 7 days to form biofilms in prepared root canals. Group I. Twelve teeth were medicated by photosensitizer (toluidine blue O) solution activated by diode lamp (FotoSan; CMS Dental, Copenhagen, Denmark).Group II. Twelve teeth were medicated by the tricr