Sharif Digital Repository

Exact Renormalization Equations (ERGE) are powerful non-perturbative tools to study the dynamics of Quantum Field theories, with respect to the change of energy. Putting cut-off on momentums of the system, is the specific regularization that is used to obtain ERGEs. This regularization breaks the gauge symmetry in the case of gauge theories. So the symmetry will be lost through the energy flow as well.Finding a gauge symmetry for a regularized system is the aim of this research. Also we have investigated the related ERGEs and the behavior of symmetry through the flow  

Most of the real-world systems can be modeled as closed loop systems which are made up of a LTI subsystem in the forward path and a memoryless nonlinear subsystem in the feedback path. Such systems are called “Lur’e systems”, the name of the first who introduced these systems. Because of the generality and the wide applicability of this type of systems, studying the stability of them has been notable and interesting to many scientists for a long time. Meanwhile, in recent decades, many scientists in physics and engineering sciences have been interested in applications of the fractional order systems and as a result focused on studying the features of the fractional order systems. An... 

According to the environmental lows and standards, wastewater of petroleum industries such as refineries and petrochemical that include many petroleum compounds like aromatic and aliphatic hydrocarbons, must be treated up to desirable limit, before entering the collecting network. Using microorganisms is one of the fundamental ways of biodegradation of these polluted compounds. Since phenolic compounds are the main components of raw petroleum, strains that are capable of tolerating phenol and usage of this poisonous hydrocarbon are specifically important. Therefore, in this study the potentiality of the indigenous thermophilic bacterium Nocardia otitidiscaviarum strain TSH1, for degradation...