In this paper a very general matrix quadratic equation is considered. This equation is known in literature as asymmetric Algebraic Riccati Equation (ARE) and arises in the solution of many problems in system and control theory and applied mathematics. For this reason a large amount of work has been produced on this topic. We present a new parametrization of the set of solutions of such equation...

In the present paper we introduce a new class of methods, Projected RungeKutta methods, for the solution of index 3 differential algebraic equations (DAEs) in Hessenberg form. The methods admit the integration of index 3 DAEs without any drift effects. This makes them particularly well suited for long term integration. Finally, implemented on the basis of the Radau5 code, the projected Runge-Ku...

One of the most fundamental problems in mathematics is to solve linear equations of the form Tf = g, where T is a linear transformation, g is known, and f is some unknown quantity. The simplest example of this comes from elementary linear algebra, which deals with solutions to matrix-vector equations of the form Ax = b. More generally, if V,W are vector spaces (or, in particular, Hilbert or Ban...

As the technology-enriched learning environments and theoretical constructs involved in instructional design become more sophisticated and complex, a need arises for equally sophisticated analytic methods to research these environments, theories, and models. Thus, this paper illustrates a comprehensive approach for analyzing data arising from experimental studies using structural equation model...

Mark Urban-Lurain, Michigan State University Mark Urban-Lurain is the Director of Instructional Technology Research & Development in the Division of Science and Mathematics Education at Michigan State University. Dr. Urban-Lurain's research interests are in theories of cognition, their impact on instructional design and applying these to the use of instructional technology. He is also intereste...

This paper treats the problem of consumption and portfolio choice in continuous time, with stochastic income that cannot be replicated by trading the available securities. The optimal controls and value functions are characterized in terms of the viscosity solution of the associated Hamilton-JacobiBellman equation, which is shown to exist and is characterized. The optimal policy is then given f...