This paper introduces the concept of fuzzy σ-ring as a generalization of fuzzy σ-algebra and basic properties; examples of this concept have been given.  As the first result, it has been proved that every  σ-algebra over a fuzzy set x*  is a  fuzzy σ-ring-over a fuzzy set x*  and construct their converse by example. Furthermore, the fuzzy ring  concept has been studied to generalize fuzzy algebra and its relation. Investigating  that the concept of fuzzy  σ-Ring is a stronger form of a fuzzy ring  that is every fuzzy σ-Ring over a fuzzy set x* is a fuzzy ring over a fuzzy set x* and construct their converse by example. In addition, the idea of the smallest, as an important property in the study of real analysis, is studied

Background: Proper cleaning and shaping of the whole root canal space have been recognized as a real challenge, particularly in oval-shaped canals.This in vitro study was conducted to evaluate and compare the efficiency of different instrumentation systems in removing of dentin debris at three thirds of oval-shaped root canals and to compare the percentage of remaining dentin debris among the three thirds for each instrumentation system. Materials and methods: Fifty freshly extracted human mandibular molars with single straight oval-shaped distal root canals were randomly divided into five groups of ten teeth each. Group One: instrumentation with ProTaper Universal hand instruments, Group Two: instrumentation with ProTaper Universal rotary

Simulation of direct current (DC) discharge plasma using
COMSOL Multiphysics software were used to study the uniformity
of deposition on anode from DC discharge sputtering using ring and
disc cathodes, then applied it experimentally to make comparison
between film thickness distribution with simulation results. Both
simulation and experimental results shows that the deposition using
copper ring cathode is more uniformity than disc cathode

In this paper, nanofluid of TiO₂/water of concentrations of 0.002% and 0.004% volume was used. This nanofluid was flowing through heat exchanger of shell and concentric double tubes with counter current flow to the hot oil. The thermal conductivity of nanofluid is enhanced with increasing concentrations of the TiO₂, this increment was by 19% and 16.5% for 0.004% and 0.002% volume respectively relative to the base fluid (water). Also the heat transfer coefficient of the nanofluid is increased as Reynold's number and nanofluid concentrations increased too. The heat transfer coefficient is increased by 66% and 49% for 0.004% and 0.002% volume respectively relative to the base fluid. This study showed that the friction

The numerical investigation has been performed to study the radiation affected steady state laminar mixed convection induced by a hot inner varied positions circular core in a horizontal rectangular channel for a fully developed flow. To examine the effects of thermal radiation on thermo fluid dynamics behavior in the eccentric geometry channel, the generalized body fitted co-ordinate system is introduced while the finite difference method is used for solving the radiative transport equation. The governing equations which used are continuity, momentum and energy equations. These equations are normalized and solved using the Vorticity-Stream function. After validating numerical results for the case without radiation, the detailed rad

The numerical investigation has been performed to study the radiation affected steady state laminar mixed convection induced by a hot inner varied positions circular core in a horizontal rectangular channel for a fully developed flow. To examine the effects of thermal radiation on thermo fluid dynamics behavior in the eccentric geometry channel, the generalized body fitted co-ordinate system is introduced while the finite difference method is used for solving the radiative transport equation. The governing equations which used are continuity, momentum and energy equations. These equations are normalized and solved using the Vorticity-Stream function. After validating numerical results for the case without radiation, the detailed radiatio

This article deals with the impact of including transverse ribs within the absorber tube of the concentrated linear Fresnel collector (CLFRC) system with a secondary compound parabolic collector (CPC) on thermal and flow performance coefficients. The enhancement rates of heat transfer due to varying governing parameters were compared and analyzed parametrically at Reynolds numbers in the range 5,000–13,000, employing water as the heat transfer fluid. Simulations were performed to solve the governing equations using the finite volume method (FVM) under various boundary conditions. For all Reynolds numbers, the average Nusselt number in the circular tube in the CLFRC system with ribs was found to be larger than that of the plain abs

In this paper, the Monte-Carlo simulation method was used to compare the robust circular S estimator with the circular Least squares method in the case of no outlier data and in the case of the presence of an outlier in the data through two trends, the first is contaminant with high inflection points that represents contaminant in the circular independent variable, and the second the contaminant in the vertical variable that represents the circular dependent variable using three comparison criteria, the median standard error (Median SE), the median of the mean squares of error (Median MSE), and the median of the mean cosines of the circular residuals (Median A(k)). It was concluded that the method of least squares is better than the