Ketercapaian dan Keterkontrolan Sistem Deskriptor Diskrit Linier Positif

A positive discrete descriptor system has been widely used in modeling economics, engineering, chemistry and others. In this research, we studied the necessary conditions and sufficient conditions for a positive discrete descriptors system is achieved positive and controlled postively. In addition, it is also studied on sufficient terms and conditions which ensure that discrete systems are null controlled. By using linear algebraic method and Inverse Drazin, this research has proved several theorems for discrete descriptors system achieved positive, controlled positively and controlled null. In addition, examples are given as illustrations to reinforce the validity of the proven theorems.

A linear-algebraic tool for conditional independence inference

In this note, we propose a new linear-algebraic method for the implication problem among conditional independence statements, which is inspired by the factorization characterization of conditional independence. First, we give a criterion in the case of a discrete strictly positive density and relate it to an earlier linear-algebraic approach. Then, we extend the method to the case of a discrete density that need not be strictly positive. Finally, we provide a computational result in the case of six variables.

Optimal Placement of Fixture Clamps: Maintaining Form Closure and Independent Regions of Form Closure

This paper addresses the problem of computing frictionless optimal clamping schemes with form closure on three-dimensional parts with planar and cylindrical faces. Given a work part with a pre-defined 3-2-1 locator scheme, a set of polygonal convex regions on the clamping faces are defined as the admissible positions of the clamps. The work part-fixture contact is assumed to be of the point-surface type. Using extended screw theory, we present a linear algebraic method that computes the sub-regions of the clamping faces such that clamps located within them are guaranteed to achieve form closure. These are termed dependent regions of form closure, since the clamps must be placed according to a precise relationship. We develop methods to compute these regions on work parts with planar and cylindrical faces. This result is incorporated into a new linear programming formulation to compute frictionless optimal clamping schemes. Clamping schemes with form closure are robust when uncertainty in knowledge of the external loads acting on the work part is present. Next, we extend the method to compute maximal independent regions of form closure. These are sub-regions of the dependent regions of form closure where the clamps can be placed completely independent of each other while maintaining form closure. When the clamps are placed within the independent regions of form closure, the clamping scheme is made robust against errors in their positions.