in this research at the first enalapril drug and its fullerene derivative were optimized. nbo calculations and nmr for the complexes were carried out at the b3lyp/6-31g* quantum chemistry level. different parameters such as energy levels, the amount of chemical shift in different atoms, the amount of homo/lumo, chemical potential (µ ), chemical hardness (η), the coefficients of hybrid bonds (π,...

Let T be a periodic time scale. The purpose of this paper is to use a modification of Krasnoselskii’s fixed point theorem due to T. A. Burton to show that the totally nonlinear dynamic equation with functional delay x△(t) =−a(t)x3(σ(t))+G ( t, x3(t), x3(t − r(t)) ) , t ∈ T, has a periodic solution. We invert this equation to construct a sum of a compact map and a large contraction, which is sui...

We provide a lower complexity bound for the satisfiability problem of a multi-agent justification logic, establishing that the general NEXP upper bound from our previous work is tight. We then use a simple modification of the corresponding reduction to prove that satisfiability for all multi-agent justification logics from there is Σ 2 -hard – given certain reasonable conditions. Our methods im...

The field of mathematical finance has gained significant attention since Black and Scholes (1973) published their Nobel Prize work in 1973. Using some simplifying economic assumptions, they derived a linear partial differential equation (PDE) of convection–diffusion type which can be applied to the pricing of options. The solution of the linear PDE can be obtained analytically. In this paper we...

Results for the π + N → Λ, Σ + K reactions in nuclear matter of Ref. [1] are presented. To evaluate the in-medium modification of the reaction amplitude as a function of the baryonic density we introduce relativistic, mean-field potentials for the initial, final and intermediate mesonic and baryonic states in the resonance model. These vector and scalar potentials were calculated using the quar...