In this paper, the attributes employed to model the constraints are called constraint attributes and those attributes involved in the objective function to be optimized are called cost-optimal attributes. The constrained clustering considered is conducted in such a way that the objective function of cost-optimal attributes is optimized subject to the condition that the imposed constraint is sat...

In this paper the analytical formulation of frequency domain analysis is reviewed, under a unifying approach, for deterministic and random dynamic loading. In the random case both stationary and nonstationary excitations are considered. It is shown how, in all cases, a complex linear system must be solved at each frequency step; if the solutions are carried on independently, the solution cost g...

The algorithms behind a toolbox for approximating Lyapunov exponents of nonlinear differential systems by QR methods are described. The basic solvers perform integration of the trajectory and approximation of the Lyapunov exponents simultaneously. That is, they integrate for the trajectory at the same time, and with the same underlying schemes, as integration for the Lyapunov exponents is carri...

Modeling atomic and molecular systems requires computation-intensive quantum mechanical methods such as, but not limited to, density functional theory (DFT) [11]. These methods have been successful in predicting various properties of chemical systems at atomistic detail. Due to the inherent nonlocality of quantum mechanics, the scalability of these methods ranges from O(N3) to O(N7) depending o...

In this paper, we consider the partial differential equations approach for valuing European and American style options on multiple assets. We use a method of lines finite element implementation available in the software package FEMLAB in order to solve the variational inequality that characterizes the American style option, as well as the partial differential equation that defines the European ...

Visualization is a method of computing by which the enormous bandwidth and processing power of the human visual (eye-brain) system becomes an integral part of extracting knowledge from complex data. In that regard, our previous work has discussed methods of appropriate mapping of user goals to the design of pictorial content by considering both the underlying data characteristics and the (human...

A dynamic Euler-Euler model for gas-liquid flows subject to mass transfer and simultaneous chemical reaction is assembled. The bubble size distribution is computed from an equation governing the evolution of average bubble mass. Highperformance finite element tools for numerical solution of the problem at hand are discussed. Computational results for the chemisorption of CO2 into NaOH shed some...

A brief outline is given of some of the main historical developments in the theory and practice of conformal mappings. Originating with the science of cartography, conformal mappings has given rise to many highly sophisticated methods. We emphasize the principles of mathematical discovery involved in the development of numerical methods, through several examples.

-The gradually increasing complexity of the processing models and necessity to simulate in higher dimensions persistently challenges computational efficiency of the modern process simulators. In this paper, an outlook on the current status and trends in numerical techniques for efficient multidimensional bulk process simulation is given. Grid generation, grid adaptation, discretization and solv...

ACKNOWLEDGEMENTS Thanks be to my collaborators and mentors for without their help I would not be here. You have all been great scholars and advisers.