We de ne a technique that is found to be useful when dealing with solution vectors (i.e., chromosomes) that must be normalized before evaluation. Normalized vectors can be either trivially manipulated or trivially interpreted, but not both. This paper studies some modi ed gradient techniques for both bit and oating point representations that have been successfully used at ARCO on some real worl...

The concept of configuration of groups which is defined in terms of finite partitions and finite strings of elements of the group is presented by Rosenblatt and Willis. To each set of configurations, a finite system of equations known as configuration equations, is associated. Rosenblatt and Willis proved that a discrete group G is amenable if and only if every possible instance of its configur...

In this paper, we introduce the novel parameters indicating Normalized Tenacity ($T_N$) and Normalized Toughness ($t_N$) by a modification on existing Tenacity and Toughness parameters.  Using these new parameters enables the graphs with different orders be comparable with each other regarding their vulnerabilities. These parameters are reviewed and discussed for some special graphs as well.

Abstract We prove the existence of a L 2 -normalized solitary wave solution for Maxwell-Dirac equations in (3+1)-Minkowski space. In addition, Coulomb-Dirac model, describing fermions with attractive Coulomb interactions mean-field limit, we (positive) energy minimizer.

This paper presents a new numerical method to solve time fractional Fokker-Planck equation. The space dimension is discretized to the Gauss-Lobatto points, then we apply pseudo-spectral successive integration matrix for this dimension. This approach shows that with less number of points, we can approximate the solution with more accuracy. The numerical results of the examples are displayed.

a theoretical solution is presented for the forced convection heat transfer of a viscoelastic fluid obeying the giesekus constitutive equation in a concentric annulus under steady state, laminar, and purely tangential flow. a relative rotational motion exists between the inner and the outer cylinders, which induces the flow. a constant temperature was set in both cylinders, in this study. the f...