In this paper, the Lifshitz formula for the Casimir energy between two dielectrics in zero temperature is derived using box RENORMALIZATION. Although there are several derivations for the force in this case in the literature, including Lifshitz’ s own proof, so far there has been no unambiguous and rigorous derivation for energy that we are aware of. Since energy becomes important in some cases, e. g. calculation of entropy or heat capacity, using the correct and precise definition of the Casimir energy, for the first time, we remove all of the infinities systematically without any ambiguity. This proof also shows the strength and accuracy of the box RENORMALIZATION scheme.

The effects of higher order excitations on the BANDGAP RENORMALIZATION of quasi-one dimensional semiconductor systems within the dynamical random phase approximation is studied. The contribution of the first and second excited states wave functions is incorporated in the calculation of the BANDGAP narrowing due to many-body exchangecorrelation effects. It is shown that incorporation of the higher order excitations leads to the result that absolute values of the BANDGAP narrowing in these cases are larger than the corresponding RENORMALIZATION which is calculated by only considering the ground state wave function.

In this paper, we investigate quantum RENORMALIZATION group theory in transverse Ising model on one dimensional chain of spin-1/2 particles. To this end, we employ recursion relations to quantum RENORMALIZATION of coherence measure at ground state. Coherence measure diagram in terms of intensity of transverse field for higher RENORMALIZATION steps shows the detection of quantum phase transition point for transverse Ising model which implies that the coherence measure can be a good indicator of quantum phase transition in transverse Ising model. Also, we obtain the divergence behavior that governs the first derivative of the coherence measure behavior, near to critical point. Although the coherence measure depends on the basis of writing the density matrix, results show that the quantum phase transition point detected by coherence measure is independent of selected basis.

The aim of this study was to examine RENORMALIZATION of Kyriacou and Sutcliffe's teachers' stress prevalence, source and symptoms scale (TSS) through factor analysis and assessing its validity and reliability. 430 male and female teachers, consisting of both physical education and non- physical education high school teachers at West Azarbaijan province filled out the TSS questionnaire. Diffluent and convergent validity of TSS were computed through determining coefficient of correlation by Mental Health Inventory (MHI) as well as Job Descriptive Index (JDI). TSS reliability was calculated through tester test and internal consistency. Reliability and validity indices obtained for TSS were satisfactory and significant at p<0.01. Seven factors were obtained by factor analysis applying varimax method. These factors had eigenvalues higher than I and 49041 percent of the total variance was explained by them. The seventh factor was removed because its reliability was lower than 0.7. The Remaining six factors are: teacher's inappropriate socioeconomic and family statues, issues concerning the school’s atmosphere and facilities, students' behavior problems and difficulties, teachers' professional qualifications, students' low amount of educational motivation and time pressure. Regarding the source and symptoms of stress, criterion validity concerning those who had stressful experiences during the past 12 months yielded that there was significance difference between two groups with low and high stress. Results showed that 8.2, 18.1, 40.0, 30.5 and 3.2 percent of the teachers were at non-risk, low risk, average risk, high risk and extreme risk areas, respectively, but none of them were at the critical area. According to the results of the research, TSS scale had necessary psychometrics characteristics to be applied at psychological research and clinical diagnosis in investigation of the teachers' stress.

New bisimide derivatives, low molecular compounds with π-π* conjugated system consisting of a pyromellitic diimide core and imine linkages were synthesized by Schiff bases reactions, the studied compounds were prepared from N,N'-bis amino pyromellitic diimide which was condensed with different derivatives of aldehydes, the materials show a high melting point and some above 300 ◦C depended intramolecular attractive and the Vander Waals attraction between various substituent groups. The optical properties of the prepared compounds were investigated by UV–vis measurement. The prepared compounds showed the highest intensity with maximum absorbance at 243-908 nm. In all studied molecules, the electrochemically estimated theoretical HOMO level is in the range of -7.515 to -7320 eV, whereas the LUMO level is close to 7.219 eV and -5.889 eV. The estimated compounds exhibited low electrochemical band gap (<2 eV).