We show how to construct a stable hierarchical basis for piecewise quadratic C continuous splines defined on Powell–Sabin triangulations. We prove that this hierarchical basis is well suited for compressing surfaces. Our compression method does not require the construction of wavelets which are usually expensive to compute, but instead we construct a stable quasi-interpolation scheme for our sp...

Particle swarm optimization (PSO) is an evolutionary algorithm known for its simplicity and effectiveness in solving various optimization problems. PSO should have strong yet balanced exploration and exploitation capabilities to enhance its performance. A superior solution guided PSO (SSG-PSO) framework integrated with an individual level based mutation operator and different local search techn...

Solar-terrestrial interactions produce a rich variety of optical emissions in the Earth’s upper atmosphere (100–1000 km). While ground based brightness measurements (i.e., column integrated photon density) provide an important diagnostic of these processes, the more interesting physics is in the associated volume emission rate distribution (i.e., photon production/cm s versus altitude). This wo...

In Fig. 1 are presented two curves of the cross section versus energy which correspond adequately to the data. Curve A is similar to the curve used by Anderson, Davidon, and Kruse. ' Curve 8 begins to rise more rapidly near 100 Mev, which may be attributed to the influence of some of the p waves. It should be noted that the difference between curves A and 8 is permitted chief by the data near 1...

A new rank-two variable-metric method is derived using Greenstadt's variational approach [Math. Comp., this issue]. Like the Davidon-Fletcher-Powell (DFP) variable-metric method, the new method preserves the positive-definiteness of the approximating matrix. Together with Greenstadt's method, the new method gives rise to a one-parameter family of variable-metric methods that includes the DFP an...

The Powell–Sabin (PS) piecewise quadratic C finite element on the PS 12-split of a triangulation is a common choice for the construction of a BPX-type preconditioner for the biharmonic equation. In this note we investigate the related Powell–Sabin element on the PS 6-split instead of the PS 12-split for the construction of such preconditioners. For the PS 6-split element multilevel spaces can b...

This paper presents a method to control the sway of a rotary crane by using a linear transfer transformation (LTT) model. The LTT model is built and its parameters are geometrically derived. Optimal control of a rotary crane is presented using an optimization method of Fletcher-Reeves so that the load has no sway at the end point of the transfer. The effectiveness of the proposed control method...

s International: Section A. Humanities and Social Sciences, 53(07), 2185A.Karcher, M. J., Davis, C., & Powell, B. (2002). The effects of develop-mental mentoring on connectedness and academic achievement. SchoolCommunity Journal, 12, 35–50.Karney, B. R., & Bradbury, T. N. (1995). The longitudinal course ofmarital quality and stability: A review of theory, methods, and resear...

We are concerned in this paper with the general problem of finding an unrestricted local minimum of a function J[xu x2 • • •, xn) of several variables xx, x2, • •., xn. We suppose that the function of interest can be calculated at all points. It is convenient to group functions into two main classes according to whether the gradient vector g, = Wbx, is defined analytically at each point or must...

In this talk we present several representation theorems and averaging theorems for members of the difference class of secant updates introduced by Broadlie, Gourlay , and Greenstadt in 1973. The BFGS update is a well-known member of this difference class. We begin with the notion of an update kernel and use it to construct a new parametrization of the difference class of secant updates. Next we...