Takeuchi [37], Takeuchi and Akahira [38] and Pfanzagl [27] among others proved that any rst-order ecient estimators are second-order ecient. Many authors e.g., Ghosh [15], have conjectured that any third-order ecient estimators are fourth-order ecient. Based on concentration probability of estimators about a true parameter, this paper gives a positive answer to the conjecture in a curved expone...

In this paper we study analytical solutions of a fourth order partial differential equation subjected to different boundary conditions of solid modelling, and investigate the effects of various factors in the PDE and boundary conditions on the shape of the generated solids. With the proposed modelling technique, we can easily manipulate and modify the shape of the generated solid by altering a ...

in this paper the periodic solutions of fourth order delay differential equation of the form $ddddot{x}(t)+adddot{x}(t)+f(ddot{x}(t-tau(t)))+g(dot{x}(t-tau(t)))+h({x}(t-tau(t)))=p(t)$  is investigated. some new positive periodic criteria are given.

This paper deals with the problem of tracking control for Takagi-Sugeno fuzzy model. An LMI (Linear Matrix Inequality) formulation is suggested to make possible the convergence of the state vector of the continuous-time system to a desired one using a new approach, called MultiQuadratic Fuzzy Lyapunov (MQFL). A fourth order unstable nonlinear system is studied to illustrate the efficiency of th...

Two formulations of a nonlinear model predictive control scheme based on the second-order Volterra series model are presented. The lirst formulation determines the control action using successive substitution, and the second method directly solves a fourth-order nonlinear programming problem on-line. One case study is presented for the SISO control of an isothermal reactor which utilizes the fi...

A new fourth order box-scheme for the Poisson problem in a square with Dirichlet boundary conditions is introduced, extending the approach in [17]. The design is based on a “hermitian box” approach, combining the approximation of the gradient by the fourth order hermitian derivative, with a conservative discrete formulation on boxes of length 2h. The goal is twofold: first to show that fourth o...

Using the Dirac constraint method we show that the pure fourth-order PaisUhlenbeck oscillator model is free of observable negative norm states. Even though such ghosts do appear when the fourth order theory is coupled to a second order one, the limit in which the second order action is switched off is found to be a highly singular one in which these states move off shell. Given this result, con...

Abstract Conformal geodesics are solutions to a system of third-order equations, which makes Lagrangian formulation problematic. We show how enlarging the class allowed variations leads variational for this with conformally invariant Lagrangian. also discuss fourth-order ODEs arising from and that some its integral curves spirals.