We investigate the generation of large scale magnetic fields in the universe from quantum fluctuations that are produced in the inflationary stage. By coupling these quantum fluctuations to the dilaton field and Ricci scalar, we show that the magnetic fields with the strength observed today can be produced. We consider two situations. First, the evolution of dilaton ends by starting the reheat...

abstract because of the many geopolitical, geo economical and geo strategically potentials and communicational capabilities of eco region, members can expand the convergence and the integration in base of this organization that have important impact on members development and expanding peace in international and regional level. based on quality analyzing of library findings and experts interv...

In this work, we calculate DGLAP evolution equation at LO and NLO by Laplace method for fragmentation function of gluon to meson or baryon. To prove the validity of this method, we evolve the fragmentation functions of  andby using this method. In this method, it is not necessary to calculate these functions in Laplace space. This method is just used for simplifing the equations

 We study the origin of subharmonic synchronization in arrays consisting of few over-damped Josephson junctions. We show that for asymmetric arrays, the evolution equations contain second (or higher) order derivatives or non-sinusoidal terms, both leading to fractional Shapiro steps in presence of external ac drive .