In this paper, it is shown that by exploiting the explicit parametric state feedback solution, it is feasible to obtain the ultimate solution to minimum sensitivity problem. A numerical algorithm for construction of a robust state feedback in eigenvalue assignment problem for a controllable linear system is presented. By using a generalized parametric vector companion form, the problem of eigen...

Multivariate control chats are generally used in situations where the simultaneous monitoring or control of two or more related quality characteristics is necessary. In most processes in the real world, distribution of the process characteristics are unknown or at least non-normal, so the non-parametric or distribution-free charts are desirable. Most non-parametric statistical process-control t...

Parametric PDE techniques, which use partial differential equations (PDEs) defined over a 2D or 3D parametric domain to model graphical objects and processes, can unify geometric attributes and functional constraints of the models. PDEs can also model implicit shapes defined by level sets of scalar intensity fields. In this paper, we present an approach that integrates parametric and implicit t...

This paper presents a numerical method for finding the solution of Plateau’s problem in parametric form. Using the properties of minimal surfaces we succeded in transfering the problem of finding the minimal surface to a problem of minimizing a functional over a class of scalar functions. A numerical method of minimizing a functional using the first variation is presented and convergence is pro...

Computation of shortest paths on free-form surfaces is an important problem in ship design, robot motion planning, computation of medial axis transforms of trimmed surface patches, terrain navigation and NC machining. The objective of this paper is to provide an e cient and reliable method for computing the shortest path between two points on a free-form parametric surface and the shortest path...

In this paper, we present a non-parametric form-finding method for designing the minimal surface, or the uniformly tensioned surface of membrane structures with arbitrary specified boundaries. The area minimization problems are formulated as distributed-parameter shape optimization problems, and solved numerically. The internal volume or the perimeter is added as the constraints according to th...

Two methods for approximating minimal surfaces in parametric form are considered. One minimizes the area of the surface, and the other the energy of the surface. The convergence of the algorithm of the first method is proved. The application of the second method to the approximation of conformai maps is examined. Several examples of computations are given.

Non-parametric classification is concerned with the classification of populations of objects when the underlying statistical model is the unknown parameter. The analysis of formal models of non-parametric classification involves the quantification of the stability of individual classes. This problem has not been solved in general. The problem of stability is discussed and a method for computing...