The BFT approach is used to formulate the electronic states in graphene through a non-commutative space in the presence of a constant magnetic field B for the first time. In this regard, we introduce a second class of constrained System, which is not gauge symmetric but by applying BFT method and extending phase space, the second class constraints converts to the first class constraints so the System becomes a gauge symmetric.

Primary standardization of radioactivity is related to the direct measurement of activity in radioactive decay. A large variety of primary standardization techniques have been developed in the past years. The photon-photon coincidence counting is one of the methods for activity determination. This method is particularly applied for the standardization of I-125 using the detection of X-ray and gamma-ray coincident counting. In this paper, a 2D photon-photon coincidence digital System with two similar ‎‎2'' × 2''‎‎ NaI(Tl) detectors for absolute activity measurement is developed. The System is established based on a 100 MHz CAEN waveform digitizer (DT5724) which directly records the pre-amplifier output signals of the two NaI(Tl) detectors. The sampled signals was transformed to trapezoidal signals using pulse height analyzer firmware and coincidence events were recorded in a list file. The list file was analyzed offline using a Matlab code to realize correlated gama lines of Co-60 source.  The Volkovitsky formulas were used for the activity calculation and the details of the experimental setup were also discussed. Standardization of  the two Co-60 standard sources was performed using this System. Results are in good agreement with the reference activity of Co-60 sources. The presented formula can be modified for absolute calibration of the other medical radioisotopes. The technique can be generalized for absolute activity measurement of I-125 which uses for ophthalmic plaque radiation therapy.

The extended finite element method (X-FEM) is a numerical method for modeling discontinuties, such as cracks, within the standard finite element framework. In X-FEM, special functions are added to the finite element approximation. For crack modeling in linear elasticity, appropriate functions are used for modeling discontinuties along the crack length and simulating the singularity in the crack tip element. As a result, the degrees of freedom (D.O.F.) for the nodes arround the crack tip and the crack length are increased, the so-called node-enrichment scheme. This virtual crack modeling, which is mesh independent, avoids the usage of refined mesh and singular elements arround the crack tip, and does not require remeshing during crack growth simulation. In this paper the principles of the X-FEM are described. A new method, based on the local orthogonal coordinate System, is proposed for the node-enrichment scheme. The development of a special-purpose computer code for modeling 2D cracks using the X-FEM and the new method is presented. The code and the new method are verified through the analyses of different standard cracked geometries.

Drip irrigation System is the efficient method of vegetable crop irrigation. This investigation is made to study water distribution horizontally and vertically in the root zone of radish crop. This study is also about leaching water below the root zone with using the modeling approach in the crop root zone. In this research laboratory and field data are used by HYDRUS-2D model. It is a high capability simulation model. Results of modeling indicated that with choice of suitable irrigation cycle (48 hour here) and emitter discharge, soil moisture is maintained at field capacity level during the whole cropping season and it decreases very slowly and supplies the required moisture for the crop. The results of water leaching and infiltration showed that leaching water below the root zone from drainage boundary compared to the total volume of water applied for the whole growing season is very low. Volume of drainage water is 0.05% of the total water used which is negligible.

Container crane is an under-actuated System, which is why it is much more difficult to control such Systems. In this paper, partial feedback linearization and sliding mode controllers are employed to control a 2D container crane with varying cable length. Since, the dynamic model of the System cannot present the real one and the System contains some uncertainties, a controller is designed to reduce the effect of model uncertainties and external disturbances. Since the considered System is under-actuated, in order to design controller, first, dynamics of the System is divided into two parts, actuated and under-actuated. Then, stability of the controllers is discussed. An objective function is considered as the combination of integral of absolute error and rate of variation of control signal. The introduced objective function is minimized employing Harmony Search and particle swarm optimization algorithms and optimum values for parameters of the designed controllers are determined to make it possible to compare performance of the mentioned controllers in their optimum conditions. Simulation results show suitable performance of the designed controllers by harmony search algorithm for the 2D crane in the presence of mass uncertainty, actuator disturbances and sensor noises.