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Bolted structures are widely utilized in industrial structures and equipment due to the numerous advantages they possess. However, the use of bolts in these structures by itself can cause considerable flaws or damages. One of the major reasons of flaw in such structures is looseness. Since the looseness is initiated with a reduction in the axial force, measurement and estimation of this force can contribute to a healthy performance of the structure. The methods used to measure axial force of bolts are divided into two: those which measure or estimate the force directly and those which, by controlling physical parameters, do this indirectly. Ba-sed on this categorization, this paper examines over 16 methods used for evaluation of axial force of bolted structures, and presents their theoretical bases, drawbacks and advantages, with the litera-ture on each method being discussed separately. Finally, the met-hods are compared and the most important criteria in selecting the methods are introduced.

Abstract. In this paper we introduce the notion of fuzzy Hilbert spaces and deduce the fuzzy version of Riesz representation theorem. Also we prove some results in fixed point theory and utilize the results to study the existence and uniqueness of solution of Uryson's integral equation.

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