We consider the loop equation in four-dimensional N = 4 SYM, which is a functional differential equation for the Wilson loop W (C) and expresses the propagation and the interaction of the string C. Our W (C) consists of the scalar and the gaugino fields as well as the gauge field. The loop C is specified by six bosonic coordinates y(s) and two fermionic coordinates ζ(s) and η(s) besides the fou...

To start with, having employed transformation wave, some nonlinear partial differential equations have been converted into an ODE. Then, using the infinite series method for equations with similar linear part, the researchers have earned the exact soliton solutions of the selected equations. It is required to state that the infinite series method is a well-organized method for obtaining exact s...

The purpose of this study is to derive optimal shapes of a body located in viscous flows by the finite element method using the acoustic velocity and the four-step explicit scheme. The formulation is based on an optimal control theory in which a performance function of the fluid force is introduced. The performance function should be minimized satisfying the state equation. This problem can be ...

BACKGROUND Many different guidelines have been presented for the construction of multiple choice items. Those guidelines have been based on the observation of errors when constructing items but not on any clear scientific criterion. Our main objective was to draw up guidelines for the development of multiple choice items based on validity criteria. METHOD We used the properties of adjustment,...

In this work, an equation of state has been utilized for thermodynamic modeling of aqueous electrolyte solutions. The proposed equation of state is a combination of simplified statistical associating fluid theory (SAFT) equation of state (similar to simplified PC-SAFT) to describe the effect of short-range interactions and mean spherical approximation (MSA) term to describe the effect of long-r...

in order to investigate the effects of piriformospora indica and trichoderma tomentosum fungi on basil (ocimum basilicum l.) growth under copper nitrate levels, a pot experiment in factorial arrangement with three replicates was done during 2012. treatments were four levels of copper nitrate (0, 100, 200 and 300 mg kg-1 of soil) and four levels of fungal coexistence (non-inoculation control, in...

In this paper, we find the exact solutions of some nonlinear evolution equations by using ( ′ G )expansion method. Four nonlinear models of physical significance i.e. the symmetric regularized longwave equation, the Klein-Gordon-Zakharov equations, the Burgers-Kadomtsev-Petviashvili equation and the nonlinear Schrödinger equation with a cubic nonlinearity are considered and obtained their exact...

Using systematic calculations in spinor language, we obtain simple descriptions of the second order symmetry operators for the conformal wave equation, the Dirac-Weyl equation and the Maxwell equation on a curved four dimensional Lorentzian manifold. The conditions for existence of symmetry operators for the different equations are seen to be related. Computer algebra tools have been developed ...

We consider nontrivial finite energy traveling waves for the Landau–Lifshitz equation with easyplane anisotropy. Our main result is the existence of a minimal energy for these traveling waves, in dimensions two, three and four. The proof relies on a priori estimates related with the theory of harmonic maps and the connection of the Landau–Lifshitz equation with the kernels appearing in the Gros...