We present a new characterization of semi-bent and bent quadratic functions on finite fields. First, we determine when a GF (2)-linear combination of Gold functions Tr(x i+1) is semi-bent over GF (2), n odd, by a polynomial GCD computation. By analyzing this GCD condition, we provide simpler characterizations of semi-bent functions. For example, we deduce that all linear combinations of Gold fu...

Semi-active base isolation system has been proposed mainly to mitigate the base drift of isolated structures while in most cases, its application causes the maximum acceleration of superstructure to be increased. In this paper, designing optimal semi-active base isolation system composed of linear base isolation system with low damping and magneto-rheological (MR) damper has been studied for co...

In this paper, we derive a nonlinear equation of corneal asphericity (Q) using the tangential radius of curvature (rt) on every semi-meridian. We transform the nonlinear equation into the linear equation and then obtain the Q-value of corneal semi-meridian by the linear regression method. We find the 360 semi-meridional variation rule of the Q-value using polynomial function. Furthermore, we co...

Using geometric methods for linearizing systems of second order cubically semi-linear ordinary differential equations and third order quintically semi-linear ordinary differential equations, we extend to the fourth order by differentiating the third order equation. This yields criteria for linearizability of a class of fourth order semi-linear ordinary differential equations, which have not bee...