Continuous logic is generalization of first order logic to a many valued logic with an infinitary truth value set. Many of the results of classic logic and it's model theory have been generalized to Continuous logic. Continuous logic not only has many uses in the mathematical analysis and in the model theory of mathematical analysis structures, but also has created new attitudes in classical model theory. Firstly, the present paper study the development of Continuous logic from Ł ukasiewicz logic. Then we have a review on some of the most important basic results of Continuous logic, including the completeness of the proof system and the compactness theorem. Finally, according to the concept of continuity with respect to the truth value set, we will introduce a kind of Continuous logic that is based on Continuous t-norm based fuzzy logics. This will lead to the introduction of two kinds of Continuous logics based on Gö del logic and product logic. Then we developed some of the results of Continuous logic suContinuous logic is generalization of first order logic to a many valued logic with an infinitary truth value set. Many of the results of classic logic and it's model theory have been generalized to Continuous logic. Continuous logic not only has many uses in the mathematical analysis and in the model theory of mathematical analysis structures, but also has created new attitudes in classical model theory. Firstly, the present paper study the development of Continuous logic from Ł ukasiewicz logic. Then we have a review on some of the most important basic results of Continuous logic, including the completeness of the proof system and the compactness theorem. Finally, according to the concept of continuity with respect to the truth value set, we will introduce a kind of Continuous logic that is based on Continuous t-norm based fuzzy logics. This will lead to the introduction of two kinds of Continuous logics based on Gö del logic and product logic. Then we developed some of the results of Continuous logic such as the compactness theorem for these two logics. h as the compactness theorem for these two logics.

Background and Aims: Root canal obturation is of great importance in root canal treatment. Its purpose is to eliminate microleakage, re-entry and growth of micro-organisms in the root canal system. The aim of this study was to compare coronal salivary microleakage in obturated root canals using lateral compaction, single cone gutta-percha and System B vertical compaction methods.Materials and Methods: In this in-vitro study, 80 single rooted, human extracted teeth were randomly divided into 3 experimental groups (n=20) and 2 positive and negative control groups (n=10). The specimens in each experimental group were obturated by using cold lateral compaction, single cone obturation, or Continuous wave of condensation (System B). After that, coronal saliva leakage was evaluated. Data were analyzed using Survival analysis and Log-rank test.Results: The results showed that all the specimens in the positive control group showed evidences of leakage during the first 7 days of study. None of the specimens in negative control group showed leakage during the 30-days period of the experiment. Survival test and Log-rank test showed that at the end of the 30 days, there was significantly less resistance to coronal salivary leakage in single cone method compared with lateral compaction (P=0.039)and Continuous wave of condensation (P=0.019) groups. No significant difference was observed between lateral compaction and System B vertical Continuous method (P=0.564).Conclusion: Based on the results of this study, lateral compaction and System B groups showed higher resistance against the coronal leakage compared with single cone group.

Background & Objectives: The lateral nasal osteotomy is an integral part of cosmetic surgery (rhinoplasty). A reproducible and predictable technique with the least complication is a significant contributor to operation success. Regarding the different techniques and instrumentation for osteotomy, this study was carried out with the aim of comparison of ecchymosis severity due to lateral osteotomy in internal Continuous and external perforated techniques in Tehran from 2004 to 2005. Materials & Methods: This clinical trial was conducted on 30 patients ( 15 males and 15 females ). The entire patients had the same situation pre and post operation. In each patient both internal and external osteotomy were performed , and ecchymosis severity due to operation was measured using a ruler on the 1st, 2nd, 3rd, 5th and 7th day following the operation. The data were analysed through SPSS (Smirnov & kolmograph, repeated measure and Wilks tests). Results: The study results indicated that the ecchymosis severity was far lower in external method than internal method (P=0.01) and it was higher in lower eyelids than in upper eyelids  (P=0.01). Ecchymosis severity was higher on the 3rd day than the other days and it gradually declined from 3rd to 7th days. Age had no significant association with ecchymosis severity while its rate was higher in men than in women (P=0.01). Conclusions: External osteotomy causes less ecchymosis severity compared to internal technique and has other advantages confirmed by other researchers. Thus, it can be introduced as a preferable educational technique.

In this paper, we develop the C-continuity via Scott Q-cotopological spaces, where Q is a commutative and integral quantale. The main results are: (1) The set of all C-compact elements of a complete Q-ordered set is irreducible complete; (2) The Scott Q-cotopology of a Q-ordered set under the fuzzy inclusion order is C-Continuous, even C-prealgebraic; (3) We establish an adjunction between the category of irreducible complete Q-ordered sets and the category of C-prealgebraic complete Q-ordered sets.

For a Banach algebra A, we introduce c: c(A), the set of all  2 A such that   : A! A is a completely Continuous operator, where   is de ned by   (a) = a
 for all a 2 A. We call A, a completely Continuous Banach algebra if c: c(A) = A . We give some examples of completely Continuous Banach algebras and a su cient condition for an open problem raised for the  rst time by J. E Gal e, T. J. Ransford and M. C. White: Is there exist an in nite dimensional amenable Banach algebra whose underlying Banach space is re exive? We prove that a re exive, amenable, completely Continuous Banach algebra with the approximation property is trivial.

For a Banach algebra A, we introduce c: c(A), the set of all  2 A such that   : A! A is a completely Continuous operator, where   is de ned by   (a) = a
 for all a 2 A. We call A, a completely Continuous Banach algebra if c: c(A) = A . We give some examples of completely Continuous Banach algebras and a su cient condition for an open problem raised for the  rst time by J. E Gal e, T. J. Ransford and M. C. White: Is there exist an in nite dimensional amenable Banach algebra whose underlying Banach space is re exive? We prove that a re exive, amenable, completely Continuous Banach algebra with the approximation property is trivial.

A new class of Continuous functions, namely s-R-Continuous functions, is introduced. The relations of s-R-continuity with continuity and other variants of continuity are discussed. Basic Properties of s-R-Continuous functions are studied. Conditions are established under which every weakly theta_cl-Continuous function is s-R-Continuous.