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Consider computing zeros z of Whittaker function Mκ,μ (z) for given κ and μ, and eigenvalues of Lamé equation for given ν and 0 < k¹ < 1, by reformulating them as eigenvalue problems of infinite symmetric tridiagonal matrices. Miyazaki et al. have demonstrated a matrix method to compute zeros of Whittaker function of the first kind Mκ,μ (z), using the three-term recurrence relations, as a difference equation regarding μ, introduced by Boersma. This method, in which the coefficient matrix is considered as a compact operator from Hilbert space ℓ² to itself, also gives an asymptotically accurate error analysis. Erdéryi et al. and Jansen have investigated matrix methods for computing eigenvalues of Lamé equation. Eigenvalue problems of infinite symmetric tridiagonal matrices are considered where the matrix itself is NOT compact and its inverse is compact in Hilbert space ℓ², with their diagonal and super- and sub- diagonal elements diverging. In this paper, we attempted to rewrite the problem of computing zeros of Mκ,μ (z) by another three-term recurrence relations, as a difference equation regarding κ. This approach fails to compute the zeros of Mκ,μ (z) although the elements of the matrix behave asymptotically as in Lamé's case. Our objective is to point out the critical difference between the two cases of Lamé equation and Whittaker function, and to supply a condition under which the matrix method works. [ABSTRACT FROM AUTHOR]

This paper concerns the strong stabilization for a typical example of underactuated robots called Acrobot, which is two-link underactuated planar robot with a single actuator driving the relative angle of two links. This paper shows the existence of strongly stabilizing controllers for the upright equilibrium point of the Acrobot by designing a specific output and employing the pole-zero relation of the linearized model around the equilibrium point. The paper presents a design method for the controllers. In terms of strong stabilization, some new features of the Acrobot are revealed and are compared with those of the cart-pendulum system. Simulation results are presented to validate the theoretical results. [ABSTRACT FROM PUBLISHER]

This paper concerns the strong stabilization for a typical example of underactuated robots called the Pendubot, which is two-link underactuated planar robot with a single actuator at the first joint. This paper shows the existence and design method of strongly stabilizing controllers for the upright equilibrium point of the Pendubot by designing a specific output and employing the pole-zero relation of the linearized model around the equilibrium point. Simulation results are presented to validate the theoretical results. [ABSTRACT FROM PUBLISHER]

The recent rise in school violence and prevalence of weapons in the hands of students in the past twenty years has led to implementing new disciplinary policies in schools? most notably, ?zero tolerance policies.? While these seemingly ?get tough on crime? policies remain popular, criticism and skepticism as to their effectiveness and appropriateness increase daily. The implementation of these policies nationwide has resulted in dramatic increases in school exclusions (suspensions and expulsions). Not only are exclusions more prevalent, but research suggests that a disproportionate number of African American and other minority students are being excluded from schools across the country. An additional concern regarding the consequences of zero tolerance policies is what happens to the students who are expelled and suspended from school ? where do they go? This paper will discuss the development of zero tolerance policies, as well as the most common criticisms and effects of these rigid disciplinary codes and their implementation. In addition, this paper will focus on the effects of alternative schooling. A recent concern in the literature is that many of the students who are excluded are never referred to an alternative program at all. In this paper we will examine this student-school gap and the role that race plays in the equation. [ABSTRACT FROM AUTHOR]