Sharif Digital Repository

In this thesis, we want to discuss about some aspects of semantics and proof theory of U logic. This logic was introduced by Ardehsir and Vaezian in 2012. U Logic was introduced with intention of unifying Sambin Basic Logic(Sambin in 1997) and Visser Basic Logic(Visser in 1981). These two basic logics are two of the most significant basic logics that were introduced. This thesis begins with addressing U logic proof system. Subsequently, we introduce three algebraic semantics for this logic. The first one was introduced by Girard for Linear logic. The second one was introduced by Sambin for Sambin Basic Logic. Then we introduce the third one specially for U logic. In fact, we have proof... 

In this thesis we will study the Σ1-provability logic of HA; to be more precise, we will review logico-mathematical preliminaries from branches such as modal logic, arithmetical theories, constructive mathematics, etc, and finally show that iHσ is a modal theory that is sound and complete for arithmetical Σ1-interpretations in HA and it is decidable  

In the region of intermediate densities of quark matter, the possibility of formation of inhomogeneous phases, such as dual chiral density wave phase exists. These kinds media can be formed in the heavy-ion collisions and in the core of dense stars. Since these media are rotating and magnetic, in this thesis we investigated the effects of a finite chemical potential, a rigid rotation and a constant magnetic field on the energy spectrum of dual chiral density wave in the context of Nambu-Jona-Lasino model. In the presence of magnetic fields, the energy spectrum of this system become asymmetric, and hence it gives rise to additional charge in the vacuum of the model. We have found that the... 

One of the most essential concepts for describing neutron stars is investigating their radial mass distribution or mass-radius relation. The aim of this thesis is to evaluate radial mass distribution of neutron stars in the presence of magnetic fields. To achieve this objective we use the Tolman- Oppenheimer-Volkoff equation of hydrostatic equilibrium for non-rotating cases and the Hartle- Thorne equations for rotating cases. olving these equations depends on determination of equation of state of neutron star in the presence of magnetic fields. For determining the corresponding equation of state, one can use QCD-like non-perturbative models, in particular Nambu-Jona- Lasinio (NJL) model. In...