Pine Flat Dam, located on King's River, east of Fresno, California, was constructed by the US Army Corps of Engineers in 1954 with height of 122 m. The dam's behavior was extensively studied in the 1970's and 1980's at the University of California at Berkeley that provide measured and calculated responses for correlation and comparison. For such purpose the dam was analyzed at action of various seismic excitations by taking in consideration linear and non-linear material properties as well and the effect of wave velocities of the rock foundation. The numerical analysis was carried out by preparation of 3D model of the dam thus applying code SOFiSTiK.

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The distribution of chewing pressure in intact tooth is from crown, across the root dentin and ends in periodontal ligament. Endodontic treatment procedure is dental procedure that is necessary when the pulp tissue is irreversible damaged, because of dental caries, dental disease or traumatic injury. When the dental structure is weakened, there is a possibility of crown or root fracture. The root vertical fracture is the third most common reason for tooth extraction in endodontic treated tooth. Endodontic procedure is successful when all the steps of dental procedure is completed.The objective of this study was to estimate whether the low taper of endodontic instrument decreases the possibility of tooth fracture and increase the percentage of tooth fracture resistance.To complete the aim of this study, were analyzed total number of 84 surveys, 42 of them were used for detail analysis. The electronic research was done using the databases as: Pub Med (Medline), Embase, Medscape, Web of Science and Cochrane Library. This study is based on review on published articles written in English language, reporting results related to the use of different intensity of conicity in endodontic treatment and the influence to tooth fracture resistance. Other inclusion criteria as date parameter of the articles was set from 2000 until 2022.The research examined in this review is of in vitro studies and FEA analysis. Some results of this research have shown that fracture resistance in endodontic treated tooth depends of quantity of dental structure. In many reviewed studies the evaluated levels of fracture, have been found to be significantly lover in groups of teeth that are endodontic treated with lover conicity, compared with the other groups of teeth that are endodontic treated with high percentage of conicity. Also, The FEA method has been successfully used in endodontics, where it has proven with the in vitro methods of study.

Variational calculus studied methods for finding maximum and minimum values of functional. It has its inception in 1696 year by Johan Bernoulli with its glorious problem for the brachistochrone: to find a curve, connecting two points A and B , which does not lie in a vertical, so that heavy point descending on this curve from position A to reach position in for at least time. In functional analysis variational calculus takes the same space, as well as theory of maxima and minimum intensity in the classic analysis .We will prove a theorem for functional where prove that necessary condition for extreme of functional is the variation of functional is equal to zero. We describe the solution of the equation of Euler with example of application, such as the problem of brachistochrone.

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