In recent decades, formalization in MATHEMATICAL structures has been developed in different areas with LOGICal nature. These MATHEMATICAL structures besides providing more precise and sufficient languages than natural ones, would be a base for constructing assistant software in these areas. One of these LOGIC-nature areas is "osool'e fegh" which is the LOGIC governing jurisprudential inferences in Islamic approaches. Hence, a MATHEMATICAL LOGIC for "osool'e fegh" would provide a useful device for both 'analyzing and comparison of jurisprudential inferences' and, 'designing assistant software'. In this paper we introduce our MATHEMATICAL LOGIC approach to "osool' e fegh". We search a determining LOGIC for "ossl'e fegh" in the formal LOGIC context, as it is in fact the "LOGIC of Fegh". After a survey on different meanings of "vajeb" and its properties, which is the basic deontic concept in "osool' e fegh" literature, we construct a formal language for "LOGIC of Fegh" according to dynamic LOGIC and formalize some jurisprudential rules in this language.

Usually two-dimensional substitution is used for the production of integrated circuits. Due to heavy use of communications, two-dimensional substitution has high losses as well as, density of elements is low in it. To resolve this problem, three-dimensional substitution method was proposed. Rather than the two-dimensional arrangement of elements in a row, elements are layout in three dimensions in this substitution. In this paper, three-dimensional substitution algorithms using order used in two-dimensional substitution, three-dimensional substitution analysis by mPL and three-dimensional substitution simultaneous with two-dimensional substitution by mPL have been studied in terms of structure and function, and a butterfly processing element (PE) and an Advanced Encryption Standard (AES) block and a wireless MIMO decoder to assess them have been implemented with the mentioned methods. . Applying these methods shows that the use of face to face integration by microbuses in communications of substitution algorithm, on average, improves the maximum clock and block speed of AES encryption to 15. 3% and the maximum clock and block speed of PE module to 22. 6% as well as the maximum clock and speed of MIMO modules to 17. 1%, while the use of these methods has led to the average reduction in power consumption of 2. 6% for the AES module and the average reduction in power of 12. 9% for the PE module and the average reduction in power consumption of 5. 1% for MIMO module.

In this work, a new MATHEMATICAL modeling of servo-pneumatic system's dynamics is presented. In this new modeling, internal forces, such as friction and external forces acting on the moving rod of actuator, such as loads or disturbances, are MATHEMATICALly modeled with their appropriate LOGIC. First, pressure distribution on two sides of moving piston is assigned to cancel out the friction force with respect to the piston velocity sense and to balance the external forces according to their acting direction. The regulation of pressure continues to provide the desired acceleration in the piston. The model of pressure valves is assumed linear. Due to the entrance of non-linear terms into the equations describing dynamics of the system, MATHEMATICAL modeling is based on sliding mode LOGIC. Also, sliding mode control algorithm is used to achieve the positioning aim. Finally, a numerical simulation is done to show the performance of the control activity in the presence of the new MATHEMATICAL modeling.

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.

We study the history and recent developments in nonelementary model theory focusing on the framework ofabstract elementary classes. We discuss the role of syntax and semantics and the motivation to generalize first order model theory to nonelementary frameworks and illuminate the study with concrete examples of classes of models.This first part introduces the main conceps and philosophies and discusses two research questions, namely categoricity transfer and the stability classification.

We study the history and recent developments in nonelementary model theory focusing on the framework ofabstract elementary classes. We discuss the role of syntax and semantics and the motivation to generalize first order model theory to nonelementary frameworks and illuminate the study with concrete examples of classes of models.This second part continues to study the question of catecoricity transfer and counting the number of structures of certain cardinality.We discuss more thoroughly the role of countable models, search for a non-elementary counterpart for the concept of completeness and present two examples: one example answers a question asked by David Kueker and the other investigates models of Peano Arithmetic and the relation of an elementary end-extension in terms of an abstract elementary class.

Aim: The purpose of this study was to determine the variations of the daily and weekly cycles of students' MATHEMATICAL LOGIC. Methods: The research was done in correlation method. The statistical population of the research was 11th grade of female students in human science in Khodabandeh city in 1396-1397. They were selected by random cluster sampling of 36 people in two classes. The test was performed for two weeks in two rounds of morning (8, 9. 30, 11) and afternoon (13, 14. 30, 16. 15). The Horn and ostburg questionnaire (1976) was used to measure the chronotype, and the parallel forms tests of researched MATHEMATICAL LOGIC were used to measure the MATHEMATICAL LOGIC. The mixed analysis of variance was used to analyze the data. Results: The results showed that there is a significant difference between the efficiency of students' MATHEMATICAL LOGIC at different hours of the day(f=4/215, p=. /0001), but the efficiency of MATHEMATICAL LOGIC was not significant in different days of the week. The efficiency difference of MATHEMATICAL LOGIC among the morning, afternoon, and evening was significant(f= 2/71, p=. /0004). The efficiency of students' MATHEMATICAL LOGIC differed significantly in terms of chronotype at different hours of the day(f= 3/028, p<. /0005). Conclusion: Regarding the differences in the efficiency of students' MATHEMATICAL LOGIC in terms of day and night rhythms as well as the individual differences in terms of chronotype, it is necessary that these results to be considered in the teaching and learning process in educational settings.

We know for LOGIC two systems: the Ancient LOGIC and the Modern LOGIC, which are inconsistent in some points of view. In this paper, I want to see if Ancient LOGIC, versus Modern LOGIC, is really one LOGIC, has one set of rules, and introduces one methodology. There are many disagreements on the number and the exact formulation of the valid rules of Ancient Predicate LOGIC. For instance, the various formulations of the Obversion and Contraposition (the congruent and the opposite) can be mentioned as evidence for the claim. Since Aristotle has not spoken of contraposition, it can be concluded that adding the two forms of contraposition to his LOGICal rules provide us with two new LOGICal systems, in which the formulations of the quantified propositions differ from that in Aristotle’s system. Also, since there have appeared different theories on Congruent Contraposition and the Obvertion between Muslim LOGICians, the number of the systems has reached the six. In this paper, introducing an exact definition for each of these systems, I present suitable formulations for the quantified propositions at the mentioned six systems.

Quantum mechanics replaced the traditional mechanics in the early twentieth century. To study Schrodinger’ s wave equation, whose position in this new mechanics is like the status of Newton’ s movement laws in traditional mechanics, numerous philosophical statements have been offered, one of which is ‘ quantum LOGIC’ . The founders of quantum LOGIC claim that on the basis of their observations in quantum level, the traditional LOGIC, which previously served as the measurement for right and wrong arguments, lacks the proper efficiency and must be replaced by one of the expressions of quantum LOGIC. In the present article, while shortly introducing quantum mechanics and quantum LOGIC, we have avoided entering the formal discussions of quantum LOGIC and used analytical method to investigate the possibility of replacing the traditional LOGIC with quantum LOGIC. According to this study, it was clarified that one must regard quantum LOGIC just as a MATHEMATICAL formulization, not an alternative LOGIC, because firstly it is dependent on a certain statement of Schrodinger’ s equation, and secondly, one must use traditional LOGIC to falsify it. Applying this LOGIC to traditional and quantum LOGIC would result in truth and falsehood of both LOGICs and not falsehood of traditional LOGIC and truth of alternative LOGIC.